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

I would connect with mortgage servicer to verify.

I would verify this, but this was the rule in 2020.- To add on to what @Sarita Scherpereel said you are still taking a risk with the city on the nonconforming unit even if you get the loan

Is there anyway possible to verify there were actually other offers especially after closing?

Verifying last 2 years of rental history very important!

Our biggest clients tend to use propstream for most of their offline marketing data then backfill it w/ deal machines 911 data (which is another way to verify the contact info of a property owner and it's really accurate). 

That was going to be my first suggestion.In the future, always verify the license of anyone you choose to do business with before signing any contract.

I know that from my rental properties, many of them are close to identical, we rehab to a uniform standard and it always amuses me to get appraisals back.

During this period check/verify everything that you want checked/verified.  

Do you verify their income?