I don’t really have the time to fix it for you but here’s what needs to happen.
The mesh has to be parented to the armature. If you move the armature the mesh should move with it. It seems that your armature is parented to the mesh (backwards)
The dynamics and logic should be done in a “physics box.” Create a box around the player mesh and assign all the logic and physic to that. Also parent the armature to that box.
Physic box controls everything
armature is a child of the physics box, armature controls the mesh
mesh is a child of the physics box.
Make sure there is nothing inside the physics box it can collide with (like your mesh). Go to the editing tab (F9), underneath mesh if there is no texture assigned to the mesh click new next to UV texture. In edit mode select any face on the mesh, click texture face tab and disable the “collision” button, select all the faces and copy to make sure none of the faces can collide.
Link an action actuator. Select your armatures, add an action actuator and set it up. Select the physics box at the same time and link a controller with the actuator.
There should be a tutorial somewhere on this.