Isn’t this abandonment and can’t she go in and change the locks after a certain amount of time?

It keeps it out of the weather and you can lock it up to keep tenants out of it if need be. 

An option to buy or MLO executed properly would hold it and lock you in. 

Went to look at it the other day and the the property is land-locked.

Once you own the property go to local bank to refinance at a locked in rate.

There can be a lot of locked up value in them, but very difficult for a new out of state investor to manage.....even for an experienced out of state investor for that matter.  

I can see through the lock hole that there is trash all over the floor.

Overall the process went pretty well, going with cash helped me lock in a decent price. 

If there are other Buckeyes out there who have some advice for a first-timer like myself, I'm all ears.

I agree with @Andrew Boettcher that your PM should not accept partial payment next month - ie: they need to be fully caught up, past balance, late fee, current rent, otherwise I'd move forward with trying to get them out, first through reason (PM let them out and find a cheaper place for them), or eviction if that falls on deaf ears.