This is usually a bad sign, the inner and outer ring of a damper is bonded with rubber, this might have deteriorated and slipped. The fix is to replace the damper or have it rebuilt.

Pull the #1 spark plug, then turn the crankshaft clockwise crank until piston is at top, ( look with a light or poke with a long screwdriver ) , look at the timing marks on the damper to see if zero or TDC lines up with the pointer. If the mark should be within a few degrees (allowing for not having the crank exactly at TDC ) I'm expecting it to be off inches.

I don't know what should be there. By looking at it, the large hole seems to be a locating point ( hollow dowel would go here ) with a smaller threaded home in the bottom.

Crankshafts don't go out of balance on their own so the problem won't be there. Is this an automatic or manual trans car? I've seen clutch covers throw a spring causing things to vibrate.