Left over clay bar
 

Can you store a clay bar and use it again after the initial use or is it better to throw it away after being used and buy another?

I would say store it away. My claybar kit came with a box to store the clay in.

Yep, put it in a ziploc, and spray a little of the liquid wax stuff that they provide in it to keep it moist. I bought one probably close to 5 years ago and it's still in good condition.