Yes, turn OFF the two battery switches when you are not using your coach. The generator uses the engine battery to start, just like the engine does. Either can be started by using the AUX switch on your dash. When you press that switch, you switch the House batteries to the engine and generator starting circuit. In an emergency, you can even hold that switch operated in order to continue driving to a repair facility.
The engine battery is 12vdc. You can remove it and take it to a local Auto-Zone, or Advanced Auto Parts stork and they can test it. They will also have replacements. Their stores will be not have sufficient parking for you to take the coach there to have them remove the battery. If you cannot remove it, or do not wish to, then go to a Wal-Mart that has an automotive section. They can do it for you, test it, and replace it if needed. If a Bounder sets for a long time without being driven, the parasite draws on the engine battery will run it down. These parasite draws are not cut off when the battery switch is turned off.
The House batteries are normally 6vdc deep cycle batteries. They are wet cells. When you remove a cell cap and look inside, you will see the fluid level. Also there will be a lower ring as part of the casing inside the hole. When adding fluid, use ONLY distilled water, and fill to the lower ring which. These batteries normally last 5 - 7 years if maintained. They are very little trouble. One way to tell if they are getting close to replacement time is to look at their sides. If the case sides are starting to bulge a bit, well, you may need to replace them in the not to far future. They are most likely Trojan T-105 batteries. I have seen them cost anywhere from $50 to $85 depending on where you are. Some folks replace them with golf cart batteries from Sam's Club.
All your batteries are charged when the engine is running. This is done from the engine alternator. There is a battery isolator in your coach that keeps the engine and house batteries isolated from each other while allowing them to all be charged by the engine alternator. Yes the generator will help charge the house (AUX) batteries, but this is done by powering the converter which does the charging. The engine alternator is much more efficient charging the batteries than the converter.
So you have a Chevy chassis. The one I had was a 97. On mine the engine air filter was located in the passenger side front wheel well. It was not hard to change the air filter if you are so inclined to do, and that could save you some money. Your engine is fuel injected so the only thing to change is the oil filter, air filter, PVC valve and spark plugs. With the few miles you have on it, you have a long way to go before needing spark plugs. The PVC in located on top of the engine toward the front left . It doesn't cost much, nor look like much, but you might want to change it. It is an easy change out. For oil filters, DO NOT use Fram filters.
The generator uses a special filter. Some will tell you that you can cross reference it to other than an Onan filter. Do as you wish, but my advice is to use only Onan filters. They have a back-flow device in their filters that some other brands do not. The Onan filter does not cost much more than other brands. A special wrench, made by Onan, is needed to change the generator filter. Without it, a big pair of channel lock pliers can be used. The generator oil drain out the bottom side near where the filter is located. There is a twist valve there and changing it is a snap. The generator has two spark plugs, one you can see and the other in the same place but on the other side of the generator and very hard to get to. Your generator has a carburetor, and air filter. Changing the air filter is no big deal. You should run the generator at least once a month under load. Start it, let it get up to speed, your transfer switch will trip and provide the generator 110vac to the coach. This only takes a minute or two. Then turn on your A/C units to put a load on the generator. If it is winter time, then use the Microwave rather than the A/C. Run the generator for 30-minutes. If your fuel is down to around 1/4 tank, the generator may not start, or may stop. That is by design so you don't run the coach out of gas in the boonies. When you let the coach set for a long time, put Stable in your fuel tank, drive around a bit to mix it, run the generator to get some of the mix into the carburetor, and you should be OK. Without Stable in the fuel, the fuel in the carburetor float bowl may go bad if not run for several months, and leave varnish deposits. That will require disassembly and cleaning of the carburetor. It is easy to avoid this just by running the generator and using Stable. You can use Stable any time of the year. It can be found at Wal-Mart and Auto Parts stores. You have a 75-gallon fuel tank which you should keep full when stored. Make sure you get enough Stable for that much fuel.
No cover is needed for your coach. It has a rubber roof. The roof will age, and discolor over time. It will also require cleaning. NEVER use anything on the rubber roof that has any petroleum product or base in it. It will destroy the rubber EPDM material. Just scrub it with spic-n-span at least twice a year.