Let's take each part of that question separately.
Of course. Anybody can sue anybody for anything.
Only if they can prove you did damage.
To protect yourself I suggest you get a decent digital camera (don't use your camera phone), you can get a good one for $75 or so, and take dated photos of the apartment, up one side and down the other inside and out, even if you have to take hundreds. Make duplicate on your computer and a back up USB Drive so you don't lose them.
That's between them and the city and probably has no bearing on your agreement to rent the place unless you can find something in your city codes that makes it illegal to collect rent on an illegal apartment. If there is nothing about that the worst that can happen to them is they get fined but that has nothing to do with your rental agreement. You can call the city and rat them out if you want. Just understand that these are your wife's parents, blood is thicker than water, and hell hath no fury like a woman scorned.
You have a month to month rental agreement, tenancy at will, and both parties are subject to the Texas landlord tenant statute:
http://www.statutes.legis.state.tx.u.../htm/PR.92.htm

