Nothing illegal about offering an updated lease and an application for good contact records.At that point if they choose to not sign new its a red flag or at least plan on this being a possible high maintenance possibility

(I don't work for them, hope this doesn't get flagged).

Those are all giant red flags. 

If it exists, that would help you to have a better understanding of it.One thing I did discover about FL insurance is that they sorta divide the state into zones and a carrier that does business in one zone may not be able to write a policy in another zone.

Does this raise any red flags with you?

It’s a red flag that twice you where denied for financial issues ...You mentioned it was a gift form family and hard to proof (ownership?)

Them moving from out of state raises questions and may be a red flag as they may move again as soon as their lease is up.

@Amanda Wilson the fact that nobody bought the building for 2 years is a red flag. 

If I see unpaid phone bills or utilities, that will raise red flags. 

Then they installed a 20ft high propane tank, so our insurance carrier cancelled us & we fought the assessment & got it down to 50% of what it was.