This is what I did so far step for step (and it didn't draw anything)
BEPUphysics is solely a physics engine has no concept of graphics; all rendering must be handled externally. The BEPUphysicsDrawer is a debug visualization library used by the BEPUphysicsDemos which could be used for testing purposes.
If you're using the BEPUphysicsDrawer, make sure that the object has been added to the drawer, that the drawer is being updated, and that the drawer is being drawn. None of it is automatic.
I generated a StaticMesh out of my Model (Which animates)
Using a StaticMesh for this purpose is probably not what you want; it will not automatically deform to match the animation and is likely not suitable for collision purposes. Graphical meshes are often far more complex than needed for physics and will degrade performance.
For example, if you wanted character physics, you'd probably want to use a CharacterController for it (source in the BEPUphysicsDemos). The actual physical body of a CharacterController is just a cylinder.
Even after I added the StaticMesh to the Space, the count of the Space's entities didn't rise.
StaticMeshes are not Entity objects. Entities are capable of velocity or force based movement. StaticMeshes, along with other StaticCollidables like InstancedMeshes, Terrains, and StaticGroups, are incapable of simulated motion.
To make the distinction clearer: static collidables are Collidables. An Entity is not a Collidable. An Entity does, however,
own an EntityCollidable (a child type of Collidable, accessible in the Entity.CollisionInformation property) which acts as the entity's proxy in the collision detection pipeline.
For deeper examples of how entities and static objects are set up, I would recommend checking out the EntityConstructionDemo and StaticMeshDemo in the BEPUphysicsDemos.