Any advice on how to push back or verify what actually needs to be done would be greatly appreciated.Thanks in advance!

I manage my out of state partners rehabs.......I would find an unbiased person to at least go behind the PM to verify everything

Off of the purchase contract, I would verify proof of funds, ask for prequalification letter from a lender if buyer is receiving a loan, with a good faith deposit.

Whenever someone has an esa I will of course allow them however I let them know up front that I use petscreening.com and they will verify the legitimacy of the letter and if comes back that they used one of the online services where you pay for the letter they are denied.  

Lender requirements for Mid-Term Rental (MTR) income vary, with many asking for 1-2 years of tax returns to verify consistent rental income.

., I will show the the physical location , concrete structure we do, money spend on HUB , money Made on HUB (next time ask to show HUBS those are public records and will not interact with the law) We have a book with all deals made in the community ... and you check, verify every single transaction!  

If not, agree they need to pay you with a different more verifiable method or you start the eviction process.I have had so many tenants with no bank accounts. 

One thing to keep in mind is it is my understanding (you would need to verify) that you get one shot per year to increase rents, but they can say no.

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

Just make sure to talk to your accountant and legal team to verify that this approach is in the best interest of your particular situation.