||the tracker once, then never again. It will just use up its internal battery and die. It won't recharge itself unless you unplug and re-plug the power bank into the tracker, every single time you wanted it to recharge. The trackimo-specific power bank has some special sauce that lets it continuously charge the device.
You could absolutely add some solar panels to the system though, I wonder if you could integrate them into the TTop shades, but not sure if enough light makes it through that glass. The products/tech are definitely out there to do that though, I think!
In regards to draining the car battery power, that isn't how the system works unless you specifically hook it up that way. That is the whole point of the battery bank setup really, to not use the car battery as reserve. If your tracker/battery bank is spliced in to accessory power, it would only charge off the car when the car/accessories are on. When the car is off, the tracker is only taking power from the battery bank, NOT the car battery. You could hook it up to the car battery if you wanted to though.