The buyer agreed to cover the cost of the new appraisal, which came in significantly above the purchase price.

About the same as if you rent it, less costs.

Should I go through with taking ownership of the property and try to salvage it for profit or do I refrain from even involving myself in the situation as it may cost more than it's worth to save it?

A quick web search shows it can cost upwards of $25,000.I'd say that if the flea-bag isn't a service dog now, it probably never will be.

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So an identical neighborhood (income, crime, school quality, etc.) can cost you as much as a $100k less on the South side simply because your neighbors are brown or black as opposed to white.this right here is the gem advice.  

Is there an easy way to divide the basement up? Each side of the duplex has access to the basement but below everything is connected together and I want to make sure no side has access to each other. The way I can ima...

They get a higher return since they are covering housing cost, have the $250k per spouse primary residence deduction in gains, is a savings account, higher leverage position, lower interest rate possible, will pay more premium for location, etc.House might be overpriced for REITs but not for home owners.  

After my P.M. costs I collect $940 or so/month. 

If you are going to do a HELOC then you must understand the cost of using those funds.