How do I make my character Jump? How do I make my character step to the plane with physics? because everytime I put a physic on my mesh it falls down.

Bounds > Box

(logic tab)bounds>box
(editing tab) center new

Should I put a physic on the mesh or in the armature? because my mesh just falls through the plane and stops at the center of the plane.

You can do two things to fix your problem. You can change the center of you object so that the center itself is very low.

Or, you can parent your armature to a cube (make sure you select compound object) and place all your movement logic on the cube itself.