My question is, can I legally rent this space?

The only real way to create a "warning" is to pursue them legally to get an arrest or to get a money judgment - both of which will show on a background check.Although, all the tenant rights advocates are pushing to STOP landlords from being able to consider criminal history in tenant screening:(

(Also, caveat to make sure this is all legal in your state as each is different)One - they are going to move out and leave a ton of stuff behind.

It is working as intended and is not a way around things.Loophole-A way of avoiding or escaping a cost or legal burden that would otherwise apply by means of an omission or ambiguity in the wording of acontract or law.

I should have clarified some of the things you pointed out though as that is common practice buying a STR anywhere to verify what permits you need and how to operate legally in the city.

It's also good for insurance and legal reasons, because you will need to indicate every adult and all persons, as well as details (like children, pets, etc.), on the lease.  

The question I have, is there a legal way to assume the mortgage since he has such a great rate?

If you need financial help, ask under the "Finance, Tax, and Legal" forum.

If you evict, how much money will it cost in legal fees, court costs, lost rent (because the tenant will probably stop paying), and vacancy while you prep and fill the vacancy?

Just get a security deposit that you hold in escrow from the seller’s net proceeds (as high as you can negotiate or is legally allowable in your area, in my area the most you can do is 1 months rent) and have the sellers sign a lease/ post closing occupancy agreement like a normal tenant.