To the OP:
There are differnt levels of Wilayat according to scholars, they are:
1. Wilayat al-Qaraba
This type of authority (Wilayat) is given to a father or paternal grandfather over minors and those who are insane (even after the age of adolescence). This authority to act as a guardian is based on relationship.
2. Wilayat al-qada¡¯
According to Imami Jurisprudence, the infallible Imam originally possessed the sole authority to judge amongst the people based upon God¡¯s law and revelation. At this time, however, a just and capable faqih may undertake this responsibility with the Imam¡¯s permission.
3. Wilayat al-Hakim
In this case, authority is given to a regular administrator of justice (hakim), to supervise the interests of a person who is unable to take care of his own affairs; such as a fool or an insane person. Whoever does not have a guardian (Wali), jurists say: al-hakim is the guardian of those who have no guardian.
4. Wilayat al-Mutlaqa (The Absolute Authority)
According to textual evidences, such as verse 6 of Chapter 33 of the Qur¡¯an, Imami scholars believe that the Prophet and Imams have divine authority over the people. The verse states that the Prophet has more rights over the believers than they have over themselves; thus his discretionary authority is effective amongst the people. This same authority, according to Shi¡¯a beliefs, is also bestowed upon the Imams.
5. Wilayat al-Usuba
According to Sunni jurists, this authority is connected to inheritance; it encompasses a class of inheritors. This category of Wilayat is not accepted by Imami scholars.
According to Imami doctrine, absolute authority (Wilayat al- Mutlaqa al-Elahiya) remains with the Absent Imam, even during his greater occultation. Therefore, in order to exercise authority, every just and capable faqih requires the sanction of the Imam, who is in turn designated by God as the possessor of absolute authority and guardianship.
Although all Imami scholars generally agree upon the doctrine of Vicegerency (Niyabat) that emphasizes the role of capable jurists as deputies of the Absent Imam, who are entrusted with a degree of his authority. However, the crucial issue is the scope and extent of this vicegerency and in which affairs the jurists have authority.
In order to clarify the dimensions of this discussion, it is necessary to examine the traditional roles and functions that qualified jurists undertake as deputies of the Imam.
source:
Shia Political Thought
(Chapter 2 under meaning of Wilayat ul Faqih)
Also to see sources from hadeeth with deeper explanation refer to this article from Ayatulah Jawad Amuli:
Wilayah
Read Paragraphs 5 and 6
Regaurding differnt views of Wilayat ul Faqih (as the head of a state), this is a complicated issue. Which I will try to do my best to explain (with sources).
There isn't any way to clearly show the differences of the Ulamah in this concept, because their differences are not fundementaly different. Democracy and Monarchy are two distinctly differnt systems that can easily be distinguished as seperate from each other. Regaurding Wilayat al Faqih and how much authority (or wilayah) the Faqih can have is not as simply understood. The over whelming majority of the Ulema (the only exception being the very very small group that doesnt believe in any form of Islamic government at all till the coming of the Imam [as] ) believe in the idea of Wilayat al Faqih, but disagree with how much authority this Faqih can have.
For example:
Coming to the views of the late Ayatullah al-Khu'i on the wilāyat of the Prophet and the Ahlul Bayt, I quote from the transcripe of his lectures in which he says:
"As for the first type of wilāyat [takviniya, universal], obviously there is no doubt in their authority over the entire creation as is clear from the ahādíth because they are the link in creation, through them [continues] the existence, and they are reason for creation [of the universe]; if it had not been for them, Allāh would not have created the people altogether, the people have been created for them, through them the people exist, and they are the means of the pouring forth [of the Divine grace].
"Actually, they have the universal authority just below that of the Creator Himself; this authority [of theirs] is like the authority of Almighty Allāh on the creation, however, it is weaker compared to the authority of Almighty Allāh on the creation."[124]
Then al-Khū'í also talks about the civil/political authority of the Prophet and the Imams, and says,
"As for the second dimension of their legislative wilāyat (at-tashrí'iyya) in the sense that they possess the authority to independently administer the properties and the lives of the people-obviously, there is no dispute on their authority of this kind...This is proven from well attested ahādíth, and in the farewell sermon [the Prophet said], 'Whomsoever's master I am, this 'Ali is his master. Do I not have more authority over the believers than they have themselves?' They said, 'Yes.'..."[125]
Ayatullāh al-Khū'í, while affirming the universal wilāyat of the Prophet and the Imams, does not deny their political authority. Actually, he goes further to say that,
"And the presumption that the history is contrary to that [in the sense that the Imams did not historically exercise their political authority]...is invalid."
Thus he concludes,
"So not exercising [the authority in the historical sense] does not prove the non-existence of the authority as is obvious."[126]
In essence, the two great jurists of the contemporary Shí'a world representing Qum and Najaf have identical views about the wilāyat of the Imams of Ahlul Bayt (a.s.). They both believe in all dimensions of wilāyat -spiritual, socio-political, and universal- of the Prophet and the Imams. The difference that existed between the two was only on the limits of the authority of a faqih (mujtahid, jurist) during the Occultation of the Present Imam (a.s.).
Imamat and Wilayat - Chapter 6
Here Sayyid Rizvi is stating that the only differnce between Imam Khomeini and Ayatullah Khoie is their understanding of what the limits of the faqih during occulation are. Since there are many differnt views of what the rights of a faqih are during occulation there will be many differnt views of what the limit of the faqih is, regaurding his rulership over the state. This has to do with what rights a mujtahid (faqih) has in making Islamic rulings. Here are some of the rights that exisit in Islamic fiqh:
i) Divine Laws (Al-Hukm as-Shari’)
This refers to a set of rules and commands legislated by God and expressed to people through the Prophet Muhammad and his successors. Hukm al-Shari’ is usually divided by Muslim Jurists into two divisions. The first part is called ‘al- ahkam al-taklifi’ which is the laws of duty and in turn divides into five divisions (obligation, prohibition, desirability, undesirability and permissibility or ‘mubah’). The second part is called ‘al-ahkam al-waz'i’ which establishes specific relationships and situations (waz') that are subject to particular divine laws. For instance, marriage, ownership, purity and uncleanness are all situations that the Islamic legal system endorses and defines in particular matters and circumstances - usually al-hukm al-waz'i is subject to particular laws of duty. Divine laws also are called the first order laws (al-ahkam al-aWaliya) because deeds and things by themselves - with no regard to temporal and unexpected accidents - are subjects to these laws and legislation of Islam.
ii) The Judge's Command (Al-Hukm al-Qadi)
Even though the legal decision of Judge (faqih) is issued with consideration of the Shari’ah and decrees of Islam, it is not a component of the Shari’ah. The judge’s role is merely the execution (tanfidh) and application of Islamic law to juridical cases. In administration of justice, the faqih as Judge does not deduce Islamic laws rather he attempts to apply the most appropriate laws to the situation.
iii) Governmental Orders (Al-Hukm al-Wilai)
Supporters of universal authority (Wilayat al-amma) do not restrict the orders (hukm) of the faqih to merely the administration of justice. As a hakim, the jurist may issue orders and it is incumbent upon all Muslims, even other fuqaha, to obey them. These include his edicts concerning the beginning of Ramadhan or the application of legal penalties (hudud). The best examples of orders that fall into this category are the governmental commands that the faqih may issue as the political leader of a society. The Wali al- faqih may issue orders regarding situations that he recognizes as affecting the interests of Islam, Muslims and Islamic laws and values. A situation may arise in which the Wali al-Faqih can issue an order based on the interest (maslahat) of the people, even though in principal the action would not otherwise be compulsory in Shari’ah.
Two crucial questions arise regarding these orders. The first concerns the nature of the order; whether the governmental command is categorized as the ‘first order’ of the Shari’ah, or as the ‘second order’ (al-akham as-sanavy). The second question concerns the scope of such orders. A faqih may issue an obligatory or prohibitive order regarding matters that are considered permissible (mubah) and for which there is no prior obligation (for doing or not doing it) in Islamic law. However, a dispute arises about whether or not the faqih may issue orders that disregard the commands of the Shari’ah. Since the answer to the latter of these questions emerges from the former, it is necessary to explain what we mean by ‘second order’ commands (akham as-sanavy).
iv) Al-Hukm al-Awaly and al-Hukm al-Sanavy
The actions that we commit according to our free will are subject to one of the following categories in Shari’ah, namely obligation (wajib), prohibition (haraam), desirability (mustahab), undesirability (makruh) and simple permissibility (mubah). These ‘first order’ laws (al-ahkam al-awaly) are determined by the law giver (hakim) upon considering the essence and natural status of deeds and things. However, in exceptional situations and under circumstances in which people should not or cannot respect previous legislations, new rulings must be issued. These temporal laws are legislated according to the demands made by exceptional situations, and are called laws of 'the second order'(al-ahkam al sanavy).
They are secondary and temporal because people must revert to obeying the first order laws as soon as the exceptional circumstances return to normal. For instance, according to Shari’ah it is not permissible for Muslims to eat “carrion” (dead animals) or the meat of animals not ritually slaughtered. It is a first order command, but in a dire situation when a person has nothing to eat at all, God permits him or her to eat such meat, this permission is a second order law. The Qur’an says:
He has only forbidden you what dies of itself, and blood, and flesh of swine, and that over which any other (name) other than (that of) Allah has been invoked, but whoever is driven to necessity, not desiring, nor exceeding the limit, no sin shall be upon him. [Chapter 2, Verse 173]
Fuqaha usually cite ‘necessity’ (ezterar), damage (zarar), distress and constriction (usr wa haraj), disorder of the Muslim's system (ekhtelal al-nidham) and compulsion (ekrah) as the major exceptional topics that demand and require second order laws, as reasons for reverting to laws of ‘the second order’. The prevailing conception amongst Imami Jurists emphasizes that the governmental orders should be issued by the faqih only in one of the aforementioned exceptional situations because al-hukm al- hukmati is but a second order command.
When we consider this opinion, the answer to the second question – which is the relationship between governmental order and Shari’ah - is very clear. In a normal situation, the faqih has no right to issue orders in opposition to obligatory (either haraam or wajib) first order laws, even if the interests (maslahat) of the Muslims demands thus. In other words, interest as such cannot justify governmental orders when they are on the contrary with Islamic obligatory laws.
However, situations in which the interest (maslahat) becomes so serious that ignorance of it could cause significant damage, distress and constriction or disorder, would allow the Wali al-Faqih to issue these orders.
Ayatollah Khomeini, in a revolutionary view, stated that although the implementation of Shari’ah is very important, it is not the ultimate goal. Islamic laws (Shari’ah) serve as a means to achieve the primary aim embodied in the protection of Islam and the extension of Justice. For him the Islamic State is not merely one part of Islam amongst others, but it is Islam itself. Consequently the significance of Islamic laws is overshadowed by the significance of protecting the Islamic system and the interest (maslahat) of Islam. He expressed the view during his lectures in Iraq - the seminary of Najaf - years before the Islamic Revolution in Iran.
After the Islamic Revolution in Iran he explored this view more explicitly. In his famous letter to Ayatollah Khamenei (the current Wali al-Faqih), he insists that the authority of the Prophet and Imams to govern is not only a first order divine law but also it has priority over others such as praying, fasting, Hajj and so on. He writes:
The government or the absolute guardianship (al- Wilayat al-mutlaqa) that is delegated to the noblest messenger of Allah is the most important divine laws and has priority over all other ordinances of the law. If the powers of the government restricted to the framework of ordinances of the law then the delegation of the authority to the Prophet would be a senseless phenomenon. I have to say that government is a branch of the Prophet's absolute Wilayat and one of the primary (first order) rules of Islam that has priority over all ordinances of the law even praying, fasting and Hajj...The Islamic State could prevent implementation of everything - devotional and non- devotional - that so long as it seems against Islam's interests[59].
Unlike conditional authority (Wilayat al-muqayada) that restricts the right of the faqih for issuing governmental orders solely in permissibility cases (mubahat), Wilayat al- mutlaqa, by definition, is a juridical view concerning the dominion of the just faqih to issue governmental orders even if it is in opposition with some obligatory Islamic laws.
As has become clear from the current discussion, the meaning of Wilayat al-mutlaqa is totally different from ‘absolutism’ and the establishment of a totalitarian and dictatorial government. Some qualifications and conditions are essential for the Wali al-Faqih such as justice, piety and the necessary socio-political perspicacity. So, if he fails to meet one of them, he will be dismissed. In the constitution of Islamic Republic of Iran a group of experts elected by people supervise and control the leader. This constitution in article 111 says:
Whenever the leader becomes incapable of fulfiling his constitutional duties, or loses one of the qualifications mentioned in Article 5 and 109, or it becomes known that he did not possess some of the qualifications initially, he will be dismissed. The authority of determination in this matter with the experts specified in Article 108.
As I indicated before, in Imami Political Jurisprudence ‘Wilayat al-mutlaqa’ is a new term. Imami fuqaha usually use other terms such as ‘Wilayat al-amma’ and ‘neyabat al- Amma’ to refer to the authority of faqih. Imam Khomeini applied the term publicly, then in 1990 it was enshrined in the constitution of Islamic Iran. Article 57 says:
The power of government in the Islamic Republic are vested in the legislature, the judiciary, and the executive powers, functioning under the supervision of the absolute religious leader and the leadership of the ummah.
Chapter 2 - Divine Laws
The question arises, does the faqih in the absense of the Imam have the right to have authority over all of these in regaurds to the state?
This creates differnt opinions among the Ulema. Which im not really qualifed to expand upon. But I should note that the most sound form (in my opinion) is that of Mutalq (complete authority of all these with the absense of the Imam) which is followed by the Islamic Republic, and from my readings its the one that has been explained in the most detail.