I'll answer your questions first:
1: HP, Dell, OCZ, MSI, Toshiba, a few others. I use HP, they aren't bad.
2: 7200 is a fair difference over 5400. Faster access times, sequential read and writes.
3: Typically, no. The solid state parts make no difference, but OD's (optical drives) and HDD's (hard disk drives) normally have their MTBF (mean time between failure) cut in half when in a laptop. Mobility sacrifices reliability for active parts.
4: Yes. Buy a new battery or request manufacturer replacement if you think the battery is dying (losing it's ability to hold a proper charge)
5: Core2Duo mobile probably 1.8 or 2GHz, 3 or 4GB of DDR2 (667 or 800MHz), HDD size of your choice, screen size of your choice (I tend to stick with 15.6's) DVD OD, 9600m GPU is what I recommend. More is too expensive, less doesn't do enough.
This is the right place
What do you consider "gaming"? that will help to determine what sort of mobile GPU is right.