I think I get where you are going with this, let me know if I am wrong.
If you want certain parts of the mesh to be separate objects, you can select all of the faces that should be part of one piece and while still in edit mode, press P, choose 'Selected' in the popup, and it should put those faces into a completely separate object. That effectively cuts the mesh into two pieces.
If you want the separate pieces to be in the same object, then you can join the two new objects in object mode by pressing Ctrl-J (or Shift-J...Alt-J? One of those...) and they will be two pieces in edit mode, but one object in object mode. There might be an easier way to separate pieces without having to put them back into one object like this, but I do not know how if there is a way.
And yes, it will be hollow. You'll have to add new faces to fill in the area where the mesh was split in two - if that is what you want.