Dont see why not, your computer does support PCIe arch so I think you should be ok... although I think you ment DDR2, but however if you didnt, then your computer only supports DDR2 memory technology.

You can use it  but that's a horrible card.  Many new games require at LEAST a GeForce 8600.

I would Recommend an ATI Radeon 6670 GDDR5 card instead.  The 530S non Tower system would be limited to

something like a Radeon 5450 Low profile.

The nvidia 8400 will work but like Speed Step says don't expect to play any games decently with it.  If you can afford an AMD HD 5570 or 6570 or 6670 they are a much better choice.