Well, that's a whole bunch of questions all at once.
(1)- For gaming, AMD vs. Intel CPU is not too much of an issue, as most games will be GPU limited with the relatively weak notebook GPUs. In addition, although I normally recommend quad cores for desktop gaming because they're so cheap and generally as high on clock speed as the dualies, for notebooks I recommend dual-core. Most of the quads are way down in clock speed, while the dual cores are a bit snappier for single-threaded or dual-core optimized stuff. Some of the newer core i series chips do have turbo though, which does pick up some slack. Battery life once dramatically favored Intel, but it's pretty much a wash right now.
(2)- Radeon 4xxx series will definitely support h.264 in VLC/etc, along with flash acceleration.
(3)- Radeon 4xxx series is a very wide range of options. New, you're probably stuck at 4200IGP, which is not very good for gaming. A 3870 mobile for example is much much faster for gaming, while being a bit older.
(4)- Being large/having a big screen doesn't neccesarily mean low battery life. It just means that more energy is being used typically. The newer LED screens are more efficient with power than the older lamp-backlit screens. Instead of looking at screen size to determine battery life, look for reviews on specific models. For example, the HP DV7 series that I am buying was tested at 3+ hours battery life while playing hd video, which is very good for a 17.3" large notebook. It had an 8-cell battery, and I guess the cells must be pretty decent.
(5)- When you're gaming, the GPU will ramp up in speed, which will eat the battery more quickly. Even under good conditions (dark room where you can turn the brightness down some), running at full speed 3d mode for a while will result in what might not be a very long running time. Will you often be unable to find an outlet to jack into while playing your game? If this is something crucial to you, it might be worth looking at the upcoming AMD fusion platform. It could be awhile before its out, but it looks to promise performance at least on the level of current midrange notebook 3d GPUs, while consuming a lot less power.
(6)- This is just my personal opinion, but 14" is a painfully small screen size for gaming, and at the $500ish price level not only will you most likely be looking at shared/integrated GPUs like Core i3 or HD4200/4250, but the resolution will be 1280x800 or 1280x768.
(7)- I see you have a 5870 in your desktop. A notebook with even 1/3 of that performance is going to cost at least a grand, and the majority of notebooks with that kind of horsepower are in the 17"+ range.
