Just how short do the chains have to be to keep the tongue from dragging
I sure hope I didn't give the impression I run around with the tongue on chains rather than properly connected.
Here's a picture of a setup where I think the chains are too loose - see Adjusting your Hitch
-- as for one with a better setup, I'll have to look around to see if I can find one.
The key, I think, is to get them as short as you can without having them bind when cornering or traversing gutters. I don't think you need to get too fussy, but then they should not be sloppy loose, especially to the point of dragging on the ground at the slightest provocation as many seem to be.
On my hitch (I know I have a pic around here somewhere, but where?) The ball mount is on a adjustable bracket that sticks a couple of inches below the ball mount. My chains cross under the ball and run alongside the bracket. I'd think that having the crossover point an inch or two under the ball should allow sufficient leeway in most situations but adjustments will vary for different situations.
For batteries, I note that many cargo trailers intended to carry a ton or more will have a lantern battery in a box for their brakes - you can find these setups in most automotive stores. On my trailer, the front jack uses the same circuit and is on a self resetting circuit breaker.