That's essentially what a plug-in hybrid is, modulo the "small."
Not exactly, Prius uses two drive trains and some fancy gearing to be able to use both engines. The gas engine actually propels the vehicle (either alone or together with the electric)
Some 'hybrids' like the Volt only have EV drivetrains. The gas engine is just a generator and does not turn any wheels. Which also means that it can be much simpler – no transmission to worry about, you can run at whatever the ideal RPM is. And so on.
Yes, the gas engine can turn the wheels.