I'm a little confused... Could you clarify:
1. A motivated seller is buying your house? That sounds really weird... (Why is he/she motivated to sell, and yet motivated to buy at the same time??)
2. You don't have your house listed, and it sounds like a private party deal. Why are realtors involved at all??
Anyway, to your question:
1. "Improvements" do increase your cost basis; "Repairs" do not. Paint, carpet, etc. typically is considered a repair.
2. Tax-wise there is no difference between your two hypothetical scenarios. Taxable amount = NET proceeds from sale - cost basis.
Edit: i before e... except in weird cases.