Typical costs of the ADU is >$250/ft for new construction (converting existing space is cheaper).  

It may be worth taking that when you find a real estate attorney and having them look over it.

I'm hoping to start my career in either metro Dallas-Fort Worth or Chicagoland, and my main priority to is to minimize my housing expense with roommates while building equity and learning how to be a competent landlord.

If you net $700K, that could put you in a position to buy around $2,800,000 worth of real estate.

My realtor did a comp search and says the home is worth about 730 with the comps in the area, I spoke to a bank in regards to Cash out refinance and I can pull out 80k (which I will use to buy another property) my mortage will be 3k per month...my only issue is that my interest rate is 3.75 on my current mortage and will be 4.6 on the refinance but will be getting rid of the fha loan.

Amidst a significant downturn in commercial property values, private investors (particularly high-net-worth individuals and family offices) are seizing the opportunity emerging as the dominant force accounting for 60% of deals over the past two years.

Even though you're in TN, it's worth checking out. 

What is the typical amount someone might ask for so that it wouldn't seem unreasonable? 

I typically do 4-10 specs per year. 

A typical budget for those would be 5% of incoming rent for each aka 15% total. 4.