by making offers you mean like a formal offer on a place like through the agent?

I have asked the tenant to email a formal letter asking to break the lease, forfeit last month's rent for April, and move out by April 30th. 

We get it form all angles; Tenants, owners, vendors, government, and lastly, WE still have ourselves and our families to take care of!

You need a formal set of books for your entity.

He stated he needed to extend the loan but refused to sign and record a formal extension. 

In the past, I have also used formal work bids to hold back security deposit, even if I could not get the person scheduled before the deposit was required to be returned. 

If you are not working with an attorney, then you probably don't have a reasonable company agreement, and aren't privy to the formalities involved with keeping your entity "valid".

Am I an actual business that needs to do things more formally at this point?

-We have heard that we are super "extra" since we rent by the room and people aren't use to being so formal with room rentals, but we have established the rules and formality from day one.

Some useful info here:https://www.opploans.com/oppu/articles/8-money-pitfalls-to-avoid-when-co-signing-a-lease/Pitfall No. 7: Not putting all roommates on the leaseFalen Cox, attorney at Cox, Rodman, & Middleton, LLCReaders should be aware that if they allow another person to live with them, even without the intent to acquire a roommate or create a landlord-tenant relationship, they may have to go through the formal eviction process if that person refuses to leave.”