To answer your questions,
Yes, you are drawing the water level down below your screen pipe. It doesn't need to be any more than a foot of screen on the bottom of the pipe.
Second- A jet pump consists of two pipes(one slightly larger than the other) with a foot valve at the bottom with the screen below that. In this configuration, the screen should only be about a foot long and about 2 feet from the bottom of the well. The white sand you see is the pump stirring up the bottom of the well. That should settle down with use.