In most cases you want the memory running at the same speed as the CPU fsb (different for Athon 64's).
Yes you can run the memory faster than the cpu, but it is of no benefit.
E.g. if you have an Athlon with a 333fsb, get DDR333 CAS2 memory, unless you plan to overclock the fsb.
You can use DDR400 but run it at 333 speeds. Useful if you plan to upgrade at a later date to a board/cpu that supports 400fsb.
Athlon 64's/FX's, get DDR400, CAS2 unless you plan to overclock by modifying multipliers and the HT bus.
No the vid card won't damage the cpu, and vice versa.
If you use two sticks of memory, get same size, speed, CAS and preferably same make! Expensive, but Corsair TwinX memory sticks are guaranteed to work together.
CAS is the latency of the memory, the lower the better. I believe CAS 2 is still the best, CAS 3 the worst.