The problem is that the property gets really hot in the summer, and it only has an attic fan.

You'll need to get good at analyzing rehab costs and predicting after-repair value (ARV) to ensure your margins are solid.To get started, immerse yourself in real estate education—read books, listen to podcasts, and use BiggerPockets to connect with experienced investors.

This is a request from the mother who is on the lease, saying 'she can't get rid of her', and as I understand through her is problematic. 

This rental income will not only help you cover your mortgage payments, but it also provides passive cash flow—one of the main reasons people get into real estate investing.

Just wondering if a quit claim will do it?

That coupled with a 5-10% seller carry could get you where you need to be. 

Local MFA returns are incredible at the moment and I'd like to get in on at least one cycle of them, if possible.At the minimum, then, I'm looking for Phoenix MFA deals... but even more specifically, I'd really prefer that the sponsors be based in Phoenix or -- even better yet -- be from Phoenix!

3) What would be the best way to get a mortgage on a new LLC, would our stake by our existing LLC create an issue for financiers?

Looking to get into Fix and Flipping after about 10 years of watching from the sidelines. 

You may also have to get your "hands dirty" in order to make these properties look nice or up to your standards.