If you have the coach plugged in to shore power there is no need to remove the batteries.
However, if you do need to remove the batteries for any reason such as replacement or servicing the battery box etc. make sure you take some good photos of the connections and make a drawing before removal. It WILL save you a few headaches.
I have mine stored inside, plugged in 24/7. I check the converter voltage regularly to ensure it is within 13.6-13.7 VDC. Higher voltage will result in excessive gassing off from the batteries and require adding distilled water often to keep them from going dry.
I have added 4 oz. of Mineral Oil to each cell (you will find a whole bunch of discussion on this subject in this forum) and I top off the batteries with distilled water about every six months or so.
As far as water, I don't drain mine Except, if I have been out to a Campground that uses well water. Some well water sources will cause a reaction with the Anode Rod in the Hot Water tank and you will get an extremely obnoxious odour from the hot water next time you use it after storage for a couple weeks or so.
I remove the house filter element for replacement at least once per year. With the element removed, I add a few ounces of Bleach to the canister, install it without the element, and run city water into the Fresh Water Tank to about 3/4 full. Then, with the city water off, I run water from the tank using the on board pump, through all systems in the coach to sanitize.
Once that's done, drain the tank and run city water through everything and flush the tank once or twice. Install a new filter and away you go for the year.
If you have filters under the sink and on an Ice Maker, you should swing the valves for these into by-pass so you don't run bleached water through them. I usually replace these annually also.
If you choose not to winterize, you should leave the slides IN during storage (less space to heat) and the furnace on set to around 45-48 with the basement heat switch turned on. I would also get a little Ceramic 1500 Watt Heater inside to supplement the furnace.
MPG is always a discussion among Motorhome Owners. Mine has an ISC Cummins 350 HP. When I first bought it (used) I averaged 6.6 MPG in the first 5000 Miles.
Then, I had to replace a cracked Exhaust Manifold so I removed the complete Exhaust System and installed a Banks Kit, new Exhaust Outlet Pipe off the Turbo to the Muffler and new OEM Muffler.
Now, running at 60-65 MPH, my average fuel consumption is 8.3 MPG. This was my average this summer over 6000 miles on our trip to Alaska where we encountered some steep terrain, varying speeds and driving conditions. Using the so called Econo Mode makes no difference IMO.
Hope this helps, these things are a learning experience. Everyday I find something new. This forum can be very helpful since chances are someone has been there, done that.
I have a pretty good stash of drawings and other information I have accumulated so if you run into trouble, please feel free to PM me and I'll try to help as best it can. Don't be shy about calling Newmar or the chassis Manufacturer either. Just have the coach S/N and or VIN Number handy. They will be very helpful.
Good Luck, enjoy your coach. These are one of the finest coaches on the road, IMHO.