Can the radioactive from the computer or microwave be physically harmful to me?

Theoretically, it can.  The thing is, you'd need really really really large doses of it for there to be ANY effect, so there's really nothing to be worried about!

They sell devices to test the leakage around the doors of microwaves. So yes, it can be harmful if the leak is sufficient enough.

Neither of them are emitting radioactive particles.  They are emitting some EM radiation, but it isn't even ionizing.  The bigger "risk" might be the microwave, but the metal screen blocks virtually all of the microwaves being generated and emitted inside of the microwave.  In a worst case scenario the microwaves could heat the water and fat in your body, but that would require a damaged microwave (door not closed, metal screen removed).  The computer emits very little radiation at all, and no more than basically any other similar electronic device (TV, stereo, etc).