I don't have either of these problems (on P21/30) so I can't be counted on as a good source of what to do about them. However, this might give you a clue as to why mine might be different.
When the keel is right up it can move laterally in the slot by a few millimeters at the back. The front rests against the roller so doesn't move. I can't say I've noticed it moving about when afloat but then I haven't spent much time on board on a rolly anchorage with the keel up. As soon as the keel is down far enough to get the full section into the aperture it can't move about as much.
When the keel is fully down it seems to wedge itself and doesn't move at all. In fact if I've let the keel go down with a thump, it sometimes needs a few turns with the winch to unwedge it before it comes up easily.
As to the rudder, the brackets (gudgeons??) that take the rudder bolts are each held by 4 bolts with (presumably) nuts on the inside. They are all still well tightened. I'm too old to be able to get down either via the quarter berth or the cockpit locker with any confidence I'd be able to reverse back out to determine whether the nuts are glassed over! If they are it should be possible to just tighten the bolts from the outside. There is a fair bit of play in the bottom bracket due to wear in the bracket holes and in the bolt and one day I'll ream out the holes and fit some more suitable bearing material. I might have to take the brackets off to do that and I shall send one of my smaller relations down to check whether the nuts will fall off if I undo the bolts!
Geoff Harwood P21/30 Cygnus