I want one with a battery pack or solar panel that runs on cellular (not WiFi) and has two way communication.

All the good ones have a robust accounting module as part of the platform, so you'll be good to go. 

I'm sure battery backups would help with that at night. 

Do you think (maybe for non-BP folks) that some fundamental content about income and taxes and the different areas of residential real estate should be included in one or mode modules, and if so, what would you suggest to cover?

Rules are good, just make them standard ones that other good landlords are doing.An example of what not to do: don't say you're going to do quarterly inspections (only do inspections every 6 months max and just say it's to change smoke detector batteries and check to see if there are any plumbing leaks and you're in and out in 5 minutes). 

We did install one lock( doorlock) and the battery has been good. 

You hate to send someone to fix the heat to find out the tenant doesn't know how to change the battery on the thermostat.... but that is the risk you take. 

There were plenty of pre-recorded modules, weekly "coaching" calls and a meet and greet event.

I can swap out my entire pump system in <30 minutes.I have tried all sorts of backups, battery, water & double units.

If you break down the box (heating or AC) there are several 'modules' that go into it.