That, my friend, is a Webasto heater. It is an auxiliary diesel fired heater that ties into the stock heating system in the bus. They are used by truckers and buses the world over as a means of keeping the cab warm at night as well as providing heat to the engine to make cold starting problems a thing of the past. The catch is that they can be expensive.
Another option would be a hydronic boiler. Use it to heat the coolant for the heating system, but I would also use a water-to-water plate style heat exchanger to give you the ability to preheat the engine with it and vice versa.
For cooling I think the typical rooftop units are your best option.
As far as electrical power is concerned a gennie will be your best bet. I wouldn't mess with batteries and inverters for your goals. Get a good Onan or similar purpose built RV generator. I think any RV dealer should be able to install it for you. They are designed to be permanently mounted and run continuously so no fears about having the kids in there.