What is eating my drywall?
Looks like termites. 


Termites travel in mud tubes and those pictures look like your drywall has lots of mudtubes.   They may not be eating the drywall (maybe the paper) but using it as a conduit to get to your wood.
That bug is a some sort of fly. It could be a dragonfly with a pair of wings missing or eaten.  A dragonfly is a predator of a termite.


But I think after some investigation, it is most likely a robber fly.

Robber Fly Pics and Information