Can I use Razer Mamba Tournament Edition or any other Razer Mouse on my Bed, Blanket, Mattress etc.?

You can't use any mouse on your bed, as they need a hard, uniform surface to work correctly. Even mice that are designed to be used on a couch will have a hard time on a bed, as the surface is often squishier (especially if you're using it on top of a blanket). I've looked into it a couple of times for customers at work, and the general consensus seems to be to just avoid using it directly on your bed.

You may want to look into finding some sort of hard, flat object like a textbook and putting a sticky-backed mousepad underneath, such as the Razer Sphex, which I've had great experiences using myself.