Without seeing your rifle in person, I can't really tell you what the problem is. As M.O.A. stated, the rear tang is supposed to be free-floating. Most folks can insert a couple of sheets of paper or perhaps an index card between the tang and the stock. If a previous owner was not careful and tried to relieve this area of the stock, they might have removed more material than necessary, thus leaving a gap.

The other thing is that the recoil lug should not be bottoming out in the stock's recoil lug cutout. So, when you place the action in the stock, especially if the action is not bedded to the stock, you might get some rocking back and forth until you tighten the action screws. That would be normal.