G'day Chaser, welcome to this great site!
Ball weight varies depending on....empty or full water tanks, gas bottles, where you store stuff and of course what you put in the front boot. I have found it to be a heavy little sucker, I don't know where Jayco get the ball weight stated in their pamphlet. I travel with full canvas annexe and outdoor table under bottom bunk (so behind axles) and don't have too much or heavy stuff in the boot.
The ball weight is the same wether you have both water tanks full or empty, so with both tanks full or empty I'm right on 250kg :eek-53: this includes the frame I made. I always travel with the rear water tank full, as well as having advantages it takes 24kg off the 250!
I haven't actually worked out how long I'd get with no solar so not sure, however it all depends on what your using and how often. There is some good information on this site regarding battery life if you search through. Here's a thread I started a while ago which tells you how many amps appliances use....could be helpful for you.
http://www.expandasdownunder.com/threads/amperage-for-appliances.2947/
Glad to hear your enjoying your new van, it is a great model
and don't have too many issues with it. You should intro yourself in the "new members" section and post up some pics.....everyone likes pics including me!
Where are you from? Hope to see you around!
Cheers.