The concern is possible lead based paint.

Now for the house you are leaving behind…I like to have this one freshly painted, and take action on any maintenance items.  

Start small with simple rehab projects like painting or landscaping to boost value without overextending.

The paint is chipped so I'm assuming there's lead paint and there will likely be asbestos and lead pipes for plumbing.

It needs new carpet, everything needs to be painted, the bathtub needs to be reglazed, and some of the outlets are still 2-prong.

I would have to do a small rehab of floors and paint and maybe new appliances.I want to do short term rental or this if possible.

For example if you asked him to only paint a wall but the wall does not look good because the drywall itself is bad - that is not his problem because you did not want the drywall fixed.Specify what it is you want done and if complete you will release the payment. if he disagrees then he may sue and then let the court decide. 

I don't understand how you can't track them down.You could stop paying HOA dues, and that will force them to contact you.As for the PM, I would instruct them to hold off on painting until the termite issue is resolved, which includes providing you with contact information of the HOA board.

We half-finished the basement, adding drywall, paint, and trim.

It is NOT like what social media or influencers try to paint, it's hard work.