Evolution: Happened or didn't / is allowed in LDS theology or isn't?
Is allowed:
Moses 3:6–7. How Did God Create Bodies for Adam and Eve?
President Spencer W. Kimball said: “Man became a living soul—mankind, male and female. The Creators breathed into their nostrils the breath of life and man and woman became living souls.
We don’t know exactly how their coming into this world happened, and when we’re able to understand it the Lord will tell us” (“The Blessing and Responsibilities of Womanhood,” Ensign, Mar. 1976, 72).
PofGP Student ManualDeath: Happened before the fall in some form or during some period (pre-garden etc) or didn't?
There was indeed no death before the Fall as is taught. However, in 2 Nephi 22 we see that a state of no death is NOT applied to the creative state before all was ready and placed into the garden. So death can exist prior to the garden state because prior to the garden state is undefined:
And now, behold, if Adam had not transgressed he would not have fallen, but he would have remained in the garden of Eden. And all things which were created must have
remained in the same state in which they were after they were created; and they must have remained forever, and had no end.
2 Nephi 2:22Also, the 1931 statement regarding pre Adamite races of man:
"The statement made by Elder Smith that the existence of pre-Adamites is not a doctrine of the Church is true. It is just as true that the statement: "There were not pre-Adamites upon the earth", is not a doctrine of the Church. Neither side of the controversy has been accepted as a doctrine at all."
Eve: Created from a rib or not?
Figurative, not literal:
“And I, God, created man in mine own image, in the image of mine Only Begotten created I him; male and female created I them.
The story of the rib, of course, is figurative.
Ensign, Mar. 1976, The Blessings and Responsibilities of Womanhood - SWKAdam and Eve: Brought from another planet/kingdom or not?
No doctrine. There is no doctrine on the manner of their physical creation or being placed on the earth (see above).
Adam and Eve: The literal parents of all humanity or not?
Depends on local or global garden state which seems to be undefined doctrinally. If local, then it is probably figurative in the sense that they are the first to Fall.
The Fall: When did it happen (looking for a date give or take a few hundred years)?
No specific revelation on the subject which is why I think this is most subject to change, but doctrinally, the Church goes with traditional Christianity which is not unreasonable. Recognizing that the Church has no specific revelation on the subject is key to understanding how the Church is not in conflict with science on this issue.
Carnivores
I think it's figurative. I think many in the Church think it's literal. Haven't been able to find anything doctrinal yet one way or the other.