For several reasons (property taxes, politics), I would prefer to begin real estate investing somewhere other than locally. 

How should I phrase my interest in the property to avoid coming across as pushy or insensitive?

I know a common practice (at least for syndications), is to create a separate LLC for the property and then raise capital once the deal is already under contract.

A tenant complaining online might indicate that the property manager handled them appropriately, so be sure to ask the manager for their side of the story.7.

If you decide to sell and find an investment property with a greater cash flow potential.A 1031 exchange would allow you to indefinitely all of the tax and use it to your advantage to reinvest into larger nicer property/properties.

Is this property in TN?

It varies a lot and depends on the vintage of the property and your tenant base. 

Only about $3k was spent to make upgrades and improvements to the property.

Seeking to connect with brokers and investors in the Central Ohio area for 30+ unit multi family properties.
Looking forward to meeting.
Jeff

We worked with a lawyer over there who is a US ex-pat who created and registered a local LLC for us, which owns our properties.