I have a couple of Dewalt 18V impact wrenches that produce 300 lb/ft torque, and they are overkill for lug nuts, so you have to be careful. A set of torque sticks is probably a good idea if you are going to carry something like that. I think the Milwaukee M18 produces north of 400 lb/ft. I just bought one of the new Ryobi 18V impacts with two speed ranges, ostensibly to carry in the truck. The Ryobi is also rated at 300 lb/ft, but the low speed range should allow more measured/careful torquing. The new Ryobi stuff is pretty good, and often on sale, so also a good value if you buy smart. As a side note, I recently started using my Dewalts to run up scissors jacks on construction projects, with great success and little physical effort. Should work just as well to lift a truck, as long as you have the right size deep socket.
you don't need much of an DC/AC converter to charge a battery.
For my Dewalts and the Ryobi, I have car chargers that plug into the cigarette lighter socket. Very convenient, and compact.