When the plumber went in, the only thing wrong was that the thermostat on the heater had to be reset by pushing a button. 

Probably a better idea would be a remote thermostat that you can control with your phone. 

I don't want to pay for a new unit when its nothing but capacitor or a thermostat, or have a short service life capacitor installed so the Tech can get a quick callback for extra work (not all Techs are top notch in diagnosis).If you intend to learn to service your own A/C units on the fly as they go down, I'd say that's probably a rather big learning curve, and will require some specialized equipment and training on how to safely do it.The rent or buy decision aside, it's best to have a couple of experienced reliable A/C techs at your disposal. 

I also don't change batteries in your smoke detector or thermostat when they go but will do a maintenance change on an inspection.

As mentioned, I have one tenant in the medium sized room and I'm in the master bedroom (fl 3) in the same unit currently, which has a supply and a return and heats up just fine.Measuring the temperatures with central heat on a cold day at 70 degrees on the thermostat it can heat the medium br to 65 and the living room to 68.

Google Nest thermostats are not user friendly for guests.

YMMV (your mileage may vary)Fixable alone: boiler maintenance and steam system rebalancing, minor lead paint sealing, plaster patching (even very large ones), thermostat installation, insulate flooring and rim joists, painting, floor repair, skim coating walls, installing thresholds, weatherproofing, installing/refinishing door and cabinet hardware, adjuster gutter drainageNeeded professionals: sewage main unclogging ($), knob and tube disconnection+removal ($$), flooring ($$), adding joists for structural support within walls ($$), replacement and removal of old brass/cast iron plumbing where necessary ($$$), new gas line for laundry and lines for appliances ($), wall demo + replacement ($$$), steam line moving and radiator repair ($$), gutters ($$)$ - hundreds, $$ - thousands, $$$ 5K-10K, $$$$ - tens of thousandsHope this helps, best of luck with the old home!

But FWIW, you can use a Yale lock and Nest thermostat and control all of it from the Nest app.

My main concern is if the pipes will freeze in winter without thermostat controlled heat.

Your hvac contractor should be able to setup a controls package to allow the two systems to interact with one another.Be advised many heat pump thermostats are more expensive then usual thermostats because they’re specially designed for that piece of equipment and you cannot use something like a nest or an ecobee.