Sheetrock damage from leaks can be a real pain, in this case, it had leaked long enough that a wide area had warped and started to sag.
The only option at this point is to rip out all the bad sheetrock (in this case about 1/3 of the living area) and tie in new bracing and install new.
A projece of this size is costly and messy.
This was an older house and it had a popcorn ceiling. A texture gun with a hopper is a must with this type of ceiling!! I would NEVER recomend buying popcorn in a spraycan or rolling it on.
Sheetrock in my opinion is tough unless you have quite a lot of experience with it, I would recomend finding a friend or relative that knows something about it and offering them a good home-cooked dinner.... or maybe 20 : )