Welcome to the board.
A lot of info left off here. Is it a diesel or gas rig? A class A or class C? How new (or old) is it.....what year? How many gallons is your fuel tank?
Either way, keep an eye on your fuel guage. For the first tank I'd try re-fueling after 2/3 tank is gone. Once you know how many miles you went and how many gallons that took, you'll have a good idea of how many miles to the gallon you're getting. Do that over two or three tank fulls and you'll have an even better idea of how many miles you can get out of a tank of fuel. By the way, any time my vehicles are sitting for more than a day or so in the winter months, I try to top off the fuel tank......to minamize the condensation in the fuel tank.
Climate controlled? Is it climate controlled or temperature controlled? I mean are they controlling relative humidity and all? Just curious what something like that costs. Tempreture controlled.....how cold does that place get down to at night? If it stays up above freezing around the clock then you shouldn't have anything to worry about. Do they have an emergency back up generator to keep it warm if they loose power? Something to think about. Even if they lost power and it got down below freezing, they'd probably have the power back on before it was a hard freeze inside.
I've only stored our boats and now our 5th wheel indoors. I believe all the indoor storage facilities here in Sacramento have a dump station on site. The two I've used (am using) have valet service so they dump for you, wash it for you, fill your fresh water tank, tire pressure, etc. if you want that done it's all included in the $127 a month. Personally, I'm skeptical that it'll be done right so I'd rather do it myself.
You may want to get the protable kennel (folding fence type thing) at any of the pet stores. They work well for keeping the dog outside without having to tie them up all the time and don't take up a lot of space when folded up.
Hope this helps a bit.