I called back ten minutes ago, here are the results of the call:
On the battery issue: He had me reset the power management system by holding down a key combination with the power off. I reset my clock, now we'll see if it did any good. I don't think it did, because the battery still shakes around in the bay, and I'm almost certain that's the problem. Try convincing him of that though... He also suggested taking it to the local Apple store to have them look at the battery.
Kernal Panic: Duh. Disk first aid. As if I hadn't thought of it before. But, I'm going to do as he suggested, so the next time I call I can say I've gone through it all, and the problem still occurs (which it will).
I kinda feel like I got brushed off a little bit. Anyway, I've got time since it's under warrenty, so I'll spend this afternoon doing all the things he suggested, wait a few days for the problems to recur, and call back. It's all I can do I guess, but it's really frustrating.
-tm