To answer some of your questions:
(Page 13) The History of the Church appears to have a few helpful entries. But since they were interpolated by later secretaries, not drawn from original records like the Prophet's journals, they cannot be used to establish the Prophet's authorship of the Lectures. furthermore, only one appears to link Joseph Smith directly to the content of the Lectures: "During the month of January [1835], I was engaged in the school of the Elders, and in preparing the lectures on theology for publication in the book of Doctrine and Covenants, which the committee appointed last September were now compiling."
Such a statement falls short of constituting acceptable historical evidence that Joseph was responsible for their content or method. Willard Richards inserted the quotation above into the record eight years after the fact; (page 14)
Also:His original diaries and journals, which for some periods provided most of the source material from which the History of the Church was later compiled, have a fifteen-month gap which spans the period in which the lectures were delivered and prepared for publication. (Page 15)
Also:Of the four members of the First Presidency (who also constituted this committee), only Oliver Cowdery and Sidney Rigdon were present for the August 17, 1835, assembly. The minutes record the absence of the other two members of the First Presidency - Joseph Smith and Frederick G. Williams. None of the twelve apostles was present either. (Page 15)
Also:Oliver Cowdery had included the statement on marriage in the 1835 edition of the Doctrine and Covenants despite Joseph's repeated requests that it not be included. (Page 18)
So, Sidney Rigdon wrote the Lectures on Faith. Joseph Smith did not endorse the Lectures on Faith.The fact that Joseph Smith's printed name leads the list of signatories to the predatory letter prepared six months earlier for that volume has led most readers to conclude that he at least endorsed the Lectures...
Given the historical record, it is perfectly possible that Joseph's role was limited to the preparation of his own revelations, which constituted the bulk of that volume. (Page 19)
This is a blow to anti mormons and break off sects.
It is a worthwhile read!