What are the sources of LDS theology that an LDS theologian need to consult to write a systematic theology?

Depperm's answer is, I think, complete, which I know isn't very satisfying relative to the level of detail you put into your question. But really the sole foundation of Latter-day Saint doctrine is the word of God revealed in the scriptures and through the prophets (ancient and modern). This, coupled with the concept of an open canon, makes it difficult to "fix" the doctrine.

That said, I will address some of your specific questions, and provide a few additional materials to depperm's list.

First to repeat depperm's list:

1. Scriptures

• Bible
• Book of Mormon
• Pearl of Great Price
• Doctrine and Covenants

2. Prophets (past/present/future)

• General Conference
• Ensign/Liahona/New Era/Friend

See also Approaching Mormon Doctrine

There are a few items which I would consider as Latter-day Saint leaders "fixing" doctrine. I use "fixing" in quotation marks because these are doctrines that were taught and set before these documents were created, these documents were more "clear, collected, and very intentional proclamations" of portions of Latter-day Saint doctrine. These do not cover all aspects of Latter-day Saint teaching, but are very good starting points.

• The Articles of Faith, dating back to Joseph Smith. This can be found within the Pearl of Great Price listed above but is of sufficient note by itself to be repeated here.

• The various proclamations and declarations listed here. I must admit I am not familiar with all of these. Those most familiar to the modern audience, and most often referred to in the church (which, not coincidentally, are the ones I am most familiar with) are as follows:

  • The Family: A Proclamation to the World, 1995, detailing doctrines related to the importance of family, both our earthly families and also the heavenly family to which we all belong.

  • The Living Christ: The Testimony of the Apostles The Church of Jesus Christ of Latter-day Saints, 2000, detailing Christ's central role as our Savior and the Son of God.

  • The Restoration of the Fulness of the Gospel of Jesus Christ: A Bicentennial Proclamation to the World., 2020, detailing doctrines related to the restoration of the gospel in the early 19th century through Joseph Smith.

I do not list the two official declarations mentioned on that website, despite them being familiar to the modern church membership, 1. in my mind they are more changes to policy than pronouncement of doctrine and 2. are also included in the Doctrine & Covenants. Official Declaration 1 from 1890 was the beginning of the end of the practice of polygamy among Latter-day Saints and Official Declaration 2 from 1978 was the announcement that all worthy men could be ordained to the priesthood, where previous there were race restrictions.

To address some of your more specific questions.

Of course the Bible and the Book of Mormon is high in the list. But what about LDS Church leaders / councils / prophets?

The prophets definitely are high on the list. This talk is good summary of how important prophets are in establishing canon. Two of the fourteen points presented in the talk are "the living prophet is more vital to us than the Standard Works [the four books of scripture listed above]" and "the living prophet is more important to us than a dead prophet." You can read the talk for details, but the short justification for those two points is that it is more valuable to have a living mouthpiece for God giving us God's word today than it is to have a record of God's word from yesterdays. That being said, the living Latter-day Saint prophets have always taught the importance of personal scripture study and often quote scripture in their addresses.

Will there be new revelations that need to be taken into account?

Yes there will be new revelations. The church's ninth Article of Faith states "We believe all that God has revealed, all that He does now reveal, and we believe that He will yet reveal many great and important things pertaining to the Kingdom of God."

What are the ranking of authority compared to the Bible & the Book of Mormon?

I think the eight Article of Faith provides the answer: "We believe the Bible to be the word of God as far as it is translated correctly; we also believe the Book of Mormon to be the word of God." As far as the Bible is translated correctly, the two books stand equal in authority.

Can there be a prophet in the future?

Yes, and not just "can there" but "there will." It is a Latter-day Saint teaching that there will be a unbroken line of prophets and apostles leading to the Second Coming.