1) The old oak tree, which had been standing in the churchyard since before the church was built, suddenly crashed to the ground.
I'd use 'had stood'
2) We slipped / crawled / sneaked down and out of the room.
(if the construction is correct which verb is best ?)
They're all fine- it depends on the way you left.
3) He shouted himself hoarse.
4) Milton read himself blind.
5) He drank himself into the grave.
6) I had to shake him awake.
7) She has already had the baby.
8) She already had the baby. (what’s the difference between 7) and 8) ?)
Both are fine- it depends on the context- if it's a recent event, I'd use 7. If you are telling me that she was a mother by the time something else in the past happened, then use 8. American speakers seem to use 'already' with the past more than British do.