They may not believe that your daughter has actually lived with you.We've seen a spike in rental application fraud, the biggest issue being residency fraud.Applicants are claiming they live with family/friends to hide their true landlord whom they haven't made payments to in months with eviction moratorium.

At the same time I'd hate to be wasting my time doing something I don't need to.Also I see how many real estate agents have their own entity (LLC) and their own website, identity sort of outside of the agency they work for.

Do not help this person commit fraud. 

Intentionally deceiving someone, in the hopes of attaining financial benefit, is fraud.

It's on a street of pretty much identical 3 2's built the same year.

I just want to avoid accidentally committing some kind of fraud. 

It’s also mortgage fraud, which can be criminally prosecuted. the reason is that the lender inherently incurs more risk when it is deemed an investment property ,therefore they command a higher investment rate. 

"offered to let me leverage his FHA"I am no legal expert, but this sounds like one of two things: 1) tip-toeing around the edges of mortgage fraud or 2) simply a bad idea. 

Signing contracts with NO MONEY OR INTENTION to close is FRAUD. 

(Or at least 1 of the 3 you identify.) not even an identical condo in the same building counts.