I know many may suggest house hacking, but I am in a unique situation where I live in a home owned by a family member where I basically pay “rent” that buys me equity in the home and I would like to continue this!

.- Do I have to ‘repay’ the purchase price from the NY-LLC to the AR-LLC?

As you've been an expat for 20 years, I imagine you may already have one that helps you navigate US filing obligations unique to expats.

I have completed over 10 deals and each one has been unique in itself.

Your family member signs an affidavit stating that you have no formal agreement worked out for repayment, and that this is strictly a gift

For example how much of the purchase/construction price do they typically finance and what do typical repayment terms look like.Thanks!

Each strategy has its own sets of unique benefits and drawbacks. 

If you have product recommendations on those I'm open.The cabinetry is kind of unique.

I would suggest contacting Hocker and Associates - they are real estate attorney plus title company so should be able to help you with any unique situation you might have.

And all 3 were unique. 1 we had a heads up on before it hit, 1 was in an area (rural and CA) where there was no competition from other investors, and 1 I had been talking to the seller as a FSBO, they ghosted me and then listed and the agent screwed up and said it was a short sale when it was not.