The delorme forums have an extensive battery test thread that will better answer your question. A general consensus seems to be that energizer lithiums give the best life of around 10-12 hours, followed by duracell 2750 nimh rechargeables at around 8 hours, I don't recall alkalines life, but seem to recall that the optional li-on battery was in the 5-6 hour range. These are all from memory so no guarantee. I personally favor the eneloop rechargeables and the duracell 2750's. As you can see they are battery hogs but I carry spares and it has never been a problem.
Yes, as long as you have a usb power adapter for your car, as the supplied cable has a usb connector for computer power. It will also charge the optional li-on battery
I believe this will all be addressed in the upcoming geocache update from delorme.
