A lot of random info, but the first map seems to be in the ballpark (without looking at all the specific cities it lists).

Question 1: If the original owners are accessing at random times to get their belongings, does this mean it's occupied in TN?

South Florida is a great place to invest but it can be random at times as far as good/bad areas and pricing.

He has random people coming and going.

You can also read your state laws concerning tax sales, to get the Real answers, not some random person's opinions, or "I heard.....".  

There are bills that will come out of the woodwork for the most random things and with a marginal return, you will negative cash flow likely until it's paid off.

I work random schedules all the time but if you have any suggestions, I'll read them here. 

If cash flow is your only goal there are much better options than some random rental house in some random location with little upside even in the best case scenarios.

I randomly plugged in a Bay Area zip code and $500k loan amount, from a random PMI company that I haven't shopped, and this came back:Break even on single premium PMI is $9200 / $170 / 12 = 4.5 years. 

It all depends on the circumstances, which is why I'm giving you random suggestions that in 'theory' could work for you.