Can I still run a background check on them at Some only require a name birthday and a prior address to run a criminal background check 

For example getting settled prior to the school year starting for their children in a new school district.

We plan to consult a tax professional but I wanted some general thoughts and considerations prior to that meeting.

Introduce yourself as the new owner with contact information, instructions for paying rent, and anything else of importance.

I make it clear that my policy is moderate (full refund prior to 5 days of arrival date), also that Airbnb has a no refund price, so that would mean no refunds under any circumstance if they book that.

You got bad advice from your prior accountant.You received rental income and it should have been reported.it seems like maybe he was lazy and/or doesn't understand rental concepts.The only exception is if he is paying 'under-market' for rent in which case the property would be considered personal use.I would fix the issue and charge him market rent. 

I would recommend negotiating prior to going into contract.

Although they had just loaned me 80k 10 months prior and im in the middle of refinancing house 3 to pay back that 80k, they agree to loan me another 200K to purchase the property to both purchase the house  and have some extra money to help with some of my own money to make make renovations.

- Paying them on time, in full, at a fair rate- Giving clear instructions, setting expectations, and providing training for relevant tasks

Last year code enforcement showed up and was "just checking on things" since they had prior history with this house & the people on the property.