No, first of all, it would be very hard to get the card out of the Xbox in the first place. Second of all, laptop cards are pretty specialized things so it probably wouldn't be compatible even if you did SOMEHOW get it out of the Xbox without damaging it. And third of all. The Xbox graphics card actually isn't that powerful, so it's really not worth all the trouble.
P.S. I'm an Xbox fanboy myself, but I have to admit the PS3 has a better graphics card.
That is not possible in any way, also laptops are very strictly made to work with the hardware it is using, even if you could buy another laptop graphics card it would not work because the PSU will not handle it.
Considering the GPU is soldered to the motherboard, I don't see any way you could do that. That is, unless you feel like you can desolder it properly, then manufacture your own board to control said GPU...