If you want it to be a business name, then I recommend you set up an LLC, transfer ownership to the LLC, and then change your leases to match the new owner name.What is your reasoning?

that we’ve learned in our 24 years, managing almost 700 doors across the Metro Detroit area, including almost 100 S8 leases.

only the appreciation gained during the leasing period?

I wish to make it official and get them on a lease. 

Just add the Tenant's Rights and Responsiblities to the end of your lease and have them sign both at the same time.

Any advice on the best way to end their lease?

In August he switched to paying 50% to 75% of rent due and stopped communicating. its a month to month lease so i had to give 30 days.

I know I need to learn all local regulations, why the property is available, if the current tenants have leases, all of the financial analyses (Let me know if any of you have come across something I might not know), section 8, available grants, and possibilities to finance the deal if the numbers work.  

I would say look through your lease which you've probably already done.

I'm guessing we end the lease, contact insurance, do repairs - then relist it for rent?