The inherited rent rates cover the hard operating expenses plus a little bit of cash that gets set aside for future maintenance/capex reserves, but no profit and not as much set aside for reserves as I'd like.The plan was always to give the inherited tenants reasonable notice to vacate (they are on month to month leases), renovate the units, and rent back out at market rate. 

Always have reserves, it took us 3 months to find our first tenant.

I plan on having cash reserves for this property.

I could put alot more cash down (20%+) but wanted to have reserves to fix anything after the house is purchased or if something breaks a year in (HVAC, water heater, repairs, fences, etc).

He said he will check his techs gps to confirm but he knows they were there because the work was done.

Talk to a lender to confirm what the requirements would be. 

I'm looking for duplexes around $100,000-150,000, so I have enough money saved up for the down payment, closing costs, and cash reserves, but the issue I have is I'm currently not employed.

I have confirmation of the tenants rent payments for the last 3 months.    

That way, I can keep cash in reserves for any major cap-ex, OR, I can use that money to make improvements to the property and charge more for rent.

Since I don't have written confirmation that they want to terminate early (and don't have the lease breaking fee), how should I proceed with them not responding?