The batmobile can't be solar powered, or at least the older iterations can't, due to what appears to be a propulsion system similar to a jet engine on the rear. I don't think he'd need to fuel it up at a gas station though, I mean, he's a multi-billionaire so nobody should really bat an eye if he decides he wants to have a tanker deliver gas directly to an underground tank at the mansion so he can fuel up there.

As far as the bat cave goes, I'd assume he does the renovations himself since we don't really see him out and about much during the day.

And for the traffic issue, I'd imagine such a rich and powerful man would have access to the traffic cameras and could have built a system into the batmobile to show him where traffic is heavy so he can avoid it. Something similar to how higher end GPS units work, but more accurate because it can use both GPS satellites and traffic cameras. Alternatively, he could just use one of those devices that let you change the traffic lights. Highly illegal, yes, but he's Batman. Why should he care about illegal?

This post has been edited by RiotDX, Wed, January 23rd, 2013 at 00:47