I am pretty sure the builder had a 1-year warranty on most “house stuff” and 10-year warranty on the foundation.I have a few small wet spots on ceiling.

Should I leave the pitched ceiling uncovered?

Tried to clean all walls, ceiling, floors, and cabinets with vinegar and even TSP.

It supplies (1500sqft)  I would suggest finding a place to frame out the supply and return downstairs on the first floor(these will be large) and go into the attic and duct down from the ceiling with flex duct.  

Also, if you want to put speakers in the ceiling or any other technology, let me know, I can help with that. 

I have a kind of an odd questions for fellow landlords or if anyone is in the insurance side.Last year when Irma hit South Florida, I suffered quite a bit of damages on a number of my rental.A particular one is a multi family building - I had fence damages, tree branch fell on roof, poked a hole through the roof, through the ceiling, debris everywhere inside, outside...so I filed a claim to my windstorm insurance carrier.I was lucky that the apartment the branch went through, was vacant at the time. 

i was going to cover it with vinyl soffit, but i saw some other houses near me that had a stained tongue and groove  porch ceiling . 

As noted you will want a full inspection done on the following: roof, sewer lines (scoped by a licensed specialist), lead paint check (specialist), test for asbestos if you have popcorn ceilings.

Interior, half the walls and ceilings are missing (lots of drywall). 

Are the ceilings one color, are the walls another color and the trim another color?