The mechanics of the deal are not too complicated, although as others have noted you can't advertise the property and then exclude people based on protected class including gender and family status....at least not legally. 

Does anyone have good experience with cold callers and where they're based out of?

My realtor commissions get paid to my LLC which is an S-Corp so I pay myself a salary based on the total of the realtor fees and other flips I do throughout the year.

Based on my experience with hoarders - Leave it alone.Unless they are causing damage you really don't want to spend your energy chasing that.

Here are some recommendations based on the limited information you posted:Yes, I would get the chimney flue installed.

The accountant that we had last time is based in Chicago, specializes in real estate and is a good one.

Usually I’m not a fan of this but there are a few exceptions.

I'll be moving to McGuire AFB in New Jersey and am looking for my first property within an hour of the base.

Do NOT buy this based on your numbers. 

Knowing your exit strategy is essential, regardless of whether your goal is to keep onto the property for the long term, sell it for a profit, or switch to another investing approach.Your choice will ultimately be based on your tastes, risk tolerance, and investing goals.