I confronted the tenant and we decided she'd pay the cat deposit and monthly pet fee.

Foreclosure properties can be acquired through a 1031 Exchange, but you need to do your homework ahead of time so that you know exactly what you will be confronted with and exactly how you will address the issue so that the only factors that are not under your control are the timing issues. 

In any event, if it were me, I would definitely confront her on what I had learned from the police. 

If the seller does ask the question, you might want to ask why they are asking the question (in a polite way, not a confrontational way).

On the other hand, I am continually confronted with this ridiculous idea that hiring out management or maintenance is necessary so that the investor will have time to find deals.

I realize it might take some confrontation to get people to respect the new situation but they shouldn't have any recourse since I own the property correct?

BUT if you decide to go the confrontational route you better be able to perform on that contract. 

The tenants are almost always home and I would prefer to avoid a face to face confrontation with them. - Can I mail the notice to quit?

We're more emotional, we're more in tune, we're less confrontational....

Incidently, when confronted today with the photos, he tried to tell my partner the huge pile of trash in the BACK YARD was probably dumped there by rogue trash dumpers who dump their trash at vacant properties!