My main concern is paying back my investors ASAP.

I just closed and was given a check in the amount of both tenants deposits.Right away you want to call and transfer any utilities that the previous owner was paying, as well as call and set up a time to introduce yourself to them, as well as lay out clear guidelines and expectations as to what to expect with you as the new owner, ie. where and when to send payment, contact info and info on what to do if there are any issues that need to be addressed.I just closed on a new duplex and acquired tenants, i called right away and started service for water and garbage for the tenants, as well as met with them in person, I showed up with a copy of their current lease agreement for them to have as a refresher, a basic rental application for them to fill out to make sure i had the most current information about employment, tenants, contact info, as well as had them make a list of concerns and things that need repair. 

Much less expensive to build duplex's per s.f. cause you avoid firewalls, sprinkler systems, ada requirements etc.

My concern is that I don't want an issue with the buyer trying to make a deal with the seller directly; since they have address, pricing etc.,.

I would demand immediately removal of the animal and I would carefully inspect the unit for any damages caused by the animal.

My plan is to call her and give her “one more chance” to see if she “accidentally” picked it up while reminding her that her lease is up.Her moving will cause her to possibly put her kids in a different school district which would be a big problem I also contacted my attorney and I am waiting to hear back from him as well. 

Chief among my concerns would probably be my ability to resell the thing, once improved and rented out.Thoughts? 

In these circumstances, I have validated that they are regularly paying all their other bills and trying to pay off their medical bills when they can and there are no other glaring concerns.

Like Vince points out, with a sandwich if your TB doesn't pay and/or causes damage, you are on the hook.

I feel like this would be pretty clear to the lender and could cause some problems.