Credit Score: 

I have great credit but limited capital.

One suggestion to consider as I mainly do BRRRRs as well- find a local bank or credit union in the area you plan to buy that offers construction loans.

With regard to my parents, I want a good relationship with them so they can build my credit history.

Incidentally, I cancelled last year when it auto renewed as well - I guess I've got to completely delete my profile and close the attached credit card for a cancellation to stick?

Local credit union.

I had belatedly realized that FHA goes off personal credit and therefore I couldn't use the LLC for it.

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

They offered to give me a credit on a future loan.

You are right, when the inspector mentioned the possibility or prior water damage is when you should of had that basement inspected by a contractor/professional and not listen to your agent.Gregg is right, the sellers were aware of some of the damage which is why they gave you a 5K credit.