As you scale your business it will become increasingly more difficult to allocate your expenses to the proper rental or business if expenses are running through your personal account.  

My question is as the new owner, does that lease still have to be honored by me or can I redraft a lease (with a lot of the same stipulations) but giving them 60 days notice of a increase in rent?

You would be better off to shop for a new manager to increase the income from the property prior to the sale.

While it was a lot of work we were able to customize the "owner's unit" to our liking, and the work we did to the other unit allowed us to increase the rent.  

There is plenty of room to increase rents and it has two newly renovated units.

The owner's own contractor even backed out. 2- My rent where I am currently living will increase significantly (by $250) in about 2 months.

Keeping it as is, only doing necessary repairs, and keep doing annual rent increases.

My last rehab the only thing that popped up is one of my contractors took on more work than they could handle and therefore were too slow pushing things back and increasing the rehab duration.I am not a fan of newbie RE investors not investing local. 

You know he will probably redeem, and you don't want to sue him and just increase his redemption charges as a result. 

Expect gradual increases.