Does radiation from the back of my laptop cause health problems if place it on my belly when I'm in my bed?

Radiation. Your laptop, like your cell phone, radio, television, etc, radiates radiation in all directions at once. The "strength" of the radiation drops dramatically, the further away you get from the source of the radiation. It shouldn't really be an issue for you. You get greater radiation exposure when you go out in the sun than you do from most modern electronic devices.