Pulling the numbers from this page, PCI moves data at a speed of about 132 Mbps while AGP 1x is twice that. AGP 8x, the current standard for video cards, passes data through at a rate of 2 Gbps (2048 Mbps), or roughly 16 times the speed of PCI. PCIe x16, which is what’s used for PCIe video cards, is 4 Gbps (4096 Mbps), or roughly 32 times the rate of PCI.
It’s possible to bridge a PCIe card to AGP; my old GeForce 6600 GT was a PCIe construction but was adapted to fit AGP. There’s simply too great a disparity to connect PCIe to PCI, though; even if it was possible (might be, I couldn’t say), it completely nullifies the card’s ability to function properly. At best, you’d have a card running at GeForce 4 levels, if that.
Yes, but you should seriously consider upping your RAM as well. Depending on your configuration (and my experience with Dell has been pretty good) you should have some open slots, so you can relatively inexpensively get to 1GB of RAM, which will help with all the non-video stuff your computer needs to do.
FWIW, the Nvidia 7600GS plays everything I want to play well, I have an Athlon XP 2.4 with 2GB of memory and an eVGA 7600GS with 256MB. I can play Oblivion, Dark Messiah, and Battlefield 2 smoothly at 1650x1080.