I'm guessing it's not a plug and play swap with the '01 SV??
From what i have herd, the top bolt is ok, the bottom one has to be trimmed as the original SV shock has a threaded joint at the bottom while the GSXR one is not. You can either get a genuine GSXR lock bolt from a dealer or trim one down.
Not from what I could find; I read it would need a different spring and re-valving. Older GSXR shock is supposed to work better, though from the charts it still seems it would still need a different spring.
There are some threads about shock options on SVrider. After some digging, found this chart that gives some good info: