If I start dating and my partner doesn't have assets/savings or may even be in debt. 

I'm NOT a lawyer and I'm only commenting to further the discussion, but my understanding of contract law means he takes possession of the property and the lease on the date of closing which means he is entitled to pro-rated rent.

You will find many of the existing home are dated, but still going for top dollar due to low inventory. 

I just have 3 questions. 1) I have a move in date on a apartments with my current girlfriend and the move in date is June 1st I mention that because, I was wondering about the residency requirements as far as the property is it a way around it or is best to just live in the property for 6 months. 2) I had one pre qualification down and I plan on doing at least 2 more before my window closes and my credit takes the hit.

Keep me up to date with your property in Memphis.

It doesn't sound like you're trying t apply pressure at all and that a reasonable date - maybe 30 days as she did pay first month (just a thought, obviously not legal advice) rent would be enough for both parties. 

I actually do not know if the tenants are up to date on rent.

Single-family home sales increased for the eleventh consecutive month, up a dramatic 47.4 percent year-over-year with 9,105 units sold;The Days on Market (DOM) figure for single-family homes dropped from 58 to 40;Total property sales rose 58.3 percent with 11,348 units sold;Total dollar volume increased 85.9 percent to about $4.0 billion;The single-family average price reached a record high, rising 20.0 percent to $371,854; The single-family median price climbed 17.6 percent to $295,000 – also a record high; Single-family homes months of inventory registered an historic low 1.4-months supply, down from 3.4 months year-over-year and below the national inventory of 2.1 months;On a year-to-date basis, single-family homes sales are running 24.4 percent ahead of 2020’s record pace.Townhome/condominium sales shot up 112.7 percent and reached record-level pricing with the average price up 8.8 percent to $246,940 and the median price up 11.0 percent to $200,000;Single-family home rentals fell 3.4 percent with the average rent up 11.0 percent to $1,960; Townhome/condominium leases rose 15.1 percent with the average rent up 8.0 percent to $1,688.HAR

I actually do not know if the tenants are up to date on rent.

Print out any emails or text messages, write down dates of phone calls and what was said, etc.You need documentation for the potential court case.