What tool should I use to cut memory foam?
For thicker pieces you might find you get better results by compressing the foam before cutting it. You could make a simple straight-line clamp out of a couple of 2x4s linked with a door hinge -- just put your foam in between, clamp the open end shut with a C-clamp, and use one edge of the wood as a guide for your cut. For your curved cuts it might make more sense to make a plywood die to match the final shape and press it down by hand or with something heavy before cutting around it.