Ok, here's your answers:
1. Minimal weight is added, and the extra battery life is very nice. You'll need the 9-Cell for a 6800 Ultra anyway, so get it.
2. The stock X300s and 6800Go run at full power even on battery.
3. Probably horrible battery life. My 6800 Go NU went for about 3:30-4 with a nine cell and everything turned down or off. Gaming I could get up to 1:45. With my 7800Go I get about 2:30 of desktop life and ~1:10 gaming. The Ultra is evidently worse on power than the 7800Go, so probably a little less than that.
4. Games run alright on battery life on my 7800Go (7800Go on battery is still faster than the 6800Go I had). Again, cant help you here because I dont own a 6800Go Ultra.
6. 9300 is great for me. Anything smaller would be a pain in the ass, I love the room and the size of the screen. The battery life is insane for such a big laptop. Also, the palm rests are big enough for me to even run my mouse on and do a little gaming (because thumbpadding it sucks
). I use my laptop to write labs and I get a good 3:30-4 hours in the library which is perfect.
I'm wondering why you went for the 6800Ultra instead of the 7800Go? The 7800 is much faster, especially in games, and it's pretty damn cheap atm at ~$250. Did you get a killer deal on the Ultra? Also, the laptop will only support 2GB of RAM, but I think that should be good for many engineering apps. Good luck