Newbie-where do you stay?
No, the battery cannot run the A/C at all, much less all night. It may be able to run a couple of small 12v fans, though. Note that if you get a diesel rig, it MAY be possible to run it all night, like the 18 wheelers do. You'd have to hear it running to find out. Just park near running 18 wheelers rather then other RVers.
Some towns have rules prohibiting overnighting, and the number is growing as a small minority of people screw things up for the rest of us. Before staying anywhere, check with the manager to ensure that it is all right, and buy something! Other possible choices are rest stops and travel/truck stops.
When you say 'Class B', you are talking about a van which has been fitted with RV stuff inside, right? I was not aware that Chrystler/Daimler had a large van, or Freightliner had any van, so I am surprized they are coming out with a 'Class B'.
No, there is no reason to run the generator (except monthly to exercise it) if you have electric hookup available.
As Jay says, storage is not critical unless you want to carry more stuff than you have room or weight capacity for, then it becomes critical. By the way, Class B RVs have very little storage capacity.
If I was going to get a class B, I'd check out Sportsmobile, who build custom Class Bs on their van or yours. Their best feature is a pop top, which greatly reduces the 'cramp' of a van, without increasing the height (during movement or storage, anyway).