I'm leaving on a 2 week riding/camping vacation in a month! And there's so much to do to get ready!

I'm getting new tires and my hard bags installed this weekend, and hopefully I'll have the bags painted some time next week. I've got my camping gear all set to go, and I've planned out where I'll be riding.
But there are still a couple things I need some advice on, which is where I turn to the collective brilliance of the forum.

A major problem I've run into is that my GPS will not charge off the battery anymore. I have a TomTom Rider 2, and it came with a charger cable that you hook to the battery. I know the unit is getting some juice, because when I hook it up, it turns on. But for whatever reason, it will not charge. Now I
know the valk battery has tons more power than a little GPS needs to charge, and I don't know what else to try. It's going to be a bummer of a trip if my GPS doesn't work (and yes, I know we've become far too reliant on them). Any ideas?
The other important thing I need to do is purchase a luggage rack for the back seat. But of course I don't know what backrest I have, and I'm not really sure how to tell. Can anyone help me out based on these pictures? What luggage rack should I look for that will fit my bike?

Any advice on these issue, or on long camping trips in general would be greatly appreciated. Thanks in advance!

-Mike