The 8800gts 320 or 640 should fit. It is the same length as a ATX board which your case can take. (the 8800GTX is 1.5" longer and may cause a problem. The bad news is that I don't think the psu is enough. Nvidia recommends 26a on the 12v rails for the whole sustem. Your psu has a 10a and a 15a 12v rail.
Depends on what other components are in your PC which will all need to run off of the 15a 12v rail.
That technically means you only have a maximum of 180w to power up your CPU, hard drives, optical drives and fans. But typically, it is not a good idea run the PSU near it's max capacity since that would increase the chances of failure. I would shoot for nothing more than 140w or about 80% of maximum.
A stock speed 8800GTS already uses 8.8a out of 10a on the other 12v rail which is nearly 90% capacity.
If you can afford to buy the 8800GTS 640, then you should have or seriously consider buying a better and more powerful PSU.
I think it will fit your case. What if I am wrong? Then you either take out the dremel, or you get another case.
I have doubts about the psu. If you try it and it is not enough, then what are the possibilities?
1) random failures?
2) component damage?
I have not installed an underpowered PSU, so I can't say from experience; what results have others seen?
When I say stock speed, I mean the the GPU core runs at 500MHz for the 8800GTS 640 to consume no more than 106w of power. Anything above that is considered an overclock and power consumption can increase very easily. It's very common for cards to be factory overclocked.