Will a PCI Express 2.0 x16 graphics card fit in a PCI Express 3.0 x8 slot, and if so, will it affect the performance? Theoretically I take it the two configurations should be equal with respect to bandwidth?
This is a very difficult thing to answer with a simple "yes/no" answer. Theoretically, with the pci-e 3.0 standard you could theoretically get nearly double-the bandwidth thanks to new encoding techniques... but that largely depends on the device being plugged into the slot. The card would fit... and it would work... but you must remember that the card will be running in 2.0 mode. (pcie-3.0 is backwards compatible with 2.0, but it won't magically make your card use the new encoding schemes that make 3.0 awesome.) This would effectively allow your card to operate as if it was plugged into an pci-e 2.0 x8 slot.
As for performance, (depending on the exact card) you would probably see a performance hit in many games and applications, but there are other applications where you may not see any difference. It really depends on what it is you're doing with the card. (for example, bitcoin mining or other similar GPU-based data processing, would probably not be affected.)