I just accept it comes with the territory and charge a pet for the wear and tear and deduct damages from SD.

It's unlikely that 2 weeks of damp drywall created anything more than moldy, mildewy drywall and if you tear it out and dry everything out that's likely the end of the story.

I am looking for a lot (smaller sized lot or lot that I could split and sell a portion) and or a property to rehab/tear down to make into my own primary residence. 

Can this GC also do any water mitigation that might be required, or will they tear this down to the slab and start over from ground-up?

It will give you an initial punch list for anything you may have missed at a turnover and also let you choose which items are still very much livable wear and tear vs items that need to be fixed eventually. 

There are cases suggesting that even just taking care of a land (e.g. by mowing, trimming, removing snow, etc.) is enough to establish adverse possession.Note that if the sewer authority needs to tear down parts of the fence to service the sewer line, it will do so regardless of who owns the land where the fence is located.  

The thought here is that since the dog is double the size, it can do double the damage/wear and tear. 

I might tear things down to the studs since I will be living there and do not like surprises.

When that occurs, I tear up the Master Agreement with them and wish them well and to be on their way.

I did lease it our for a month last winter to help a guy out, fully furnished, which helped a lot on income, but the wear and tear was a LOT higher.