Schematics are unlikely to exist. You'd probably have to trace everything out and draw them up yourself.
What number is on those parts to tell you they are mosfets? (knowing what part they are, you can replace them to see if that fixes it)
If they are simply being turned on by a faulty software or other hardware issue, it won't change anything, but if they are stuck on because they failed then replacing them will fix it. If you use parts with better specs than the originals, then it would be less likely to fail in that way again. (depends on the reason it did fail).
BTW, if your battery was truly totally drained (down to 0V? but even below safe cutoff levels is bad) then the cells are damaged and should be completely replaced*** not reused, so it's likely to be cheaper to buy a whole new battery with BMS than to do any repairs on this one.
***If you don't replace them, then the battery could fail catastrophically (fire, etc) at any moment in the future if a damaged cell fails in the wrong way. You cannot know if any cell is damaged this way until it does fail, and it's too late then. You can't predict whether or not it will fail this way, so it's not safe to reuse cells drained too far.
Fire is a low-chance but extremely high damage failure risk, so unless you're prepared to deal with the loss of everything (and everyone) involved in any fire that does happen, it's safer to not risk at all.
