•Before I started my inspection, he asked me to sit down and proceeded to make several confessions.- His lease is for himself and his adult son (a police officer), but for the last several months his adult daughter and her 5 year old child have been living in the home, and will continue to indefinitely

In order to defer all taxes you must purchase at least as much as your net sale (contract price less commissions and costs of closing) and you must use all of the net proceeds (net sales amount less debt pay off) in the next purchase or purchases.  

What will the cash out proceeds be used for?

There is usually NOTHING anyone can do most times (the only thing I'd say to agree with these statements is make sure the ball is always in the bank's court and get anything/everything back to them ASAP.

Wouldn't hurt to check with an attorney, but I think you should be entitled to withold the last month's rent from the security deposit.I doubt that "afraid to live there" would hold up in court as a reason to break the lease unless the tenant could prove the unit is not secure. 

My lease prohibits all modifications and improvements, but if the tenant proceeds anyway, they become my property.Reminding them of such, usually deters such changes.

On the sale side, title, escrow, and most closing costs are paid from proceeds of escrow so they do not come out of your pocket and thus, do not factor into your ROI equation.

This will straddle two tax years and that's another situation that will work to your advantage reporting wise and is a phrase that tax courts have used in the past to describe a valid exchange.  

I just finished purchasing my next project at the court house steps and will get started with the rehab soon.

We proceeded to buy another house, much bigger on the other side of town, in Orchards, if your familiar with the Couve.