Illustrator :: How To Add Gradient Across Multiple Nested Circles

Here is the image I am working on:

I need to know how to make it look like this:
 
There are two things going on in the origina: the S-shaped semi-transparent overlay, and a linear gradient that lightens on the top and bottom and darkens in the middle. Also, note the transparent space between the "outline shape" and the inner circles.
 
So - two things. 1) How do I apply a gradient to the entire shape, and 2) put the all-white overlay on top (overlay should be confined to the shape as well).