The answers depend somewhat on various things, like where you are and what sort of converter you have have in the motorhome and whether or not you have electric power (or installed solar) available where it's parked.
Generally speaking, it's fine to leave the batteries in the RV over the winter, doubly so if you have power (or solar) available. If it's an old single stage converter, it would be a good idea to check what sort of voltage it puts out and if it's too high (above about 13.5V, say) only have it on sporadically and check the battery water level from time to time.
If you don't have power but are in a cold (freezing) climate, charging the batteries and then disconnecting them entirely is perfectly okay; they won't self-discharge much at all over the winter unless they were practically dead already, and they won't freeze unless they are discharged or you live somewhere north of the Arctic circle.
It's a good idea to run the generator every once and again, preferably on a not too cold day, to keep varnish junk from forming in and clogging the carburetor and to keep the rings and brushes clean and working well.
It's not at all useful to run the main engine unless you have reason to drive somewhere; cold starts are relatively hard on the engine, and idling for any reasonable period of time will not bring the oil up to full operating temperature to drive off any moisture (but running it will encourage more moisture to collect in it and in the exhaust system). There's no carburetor to get gummed up, assuming you don't have a decades old motorhome.
I would suggest putting an appropriate amount of fuel stabilizer in the tank and filling it completely before storage to minimize the gas getting old and getting water condensed into it.
