1. Wandering shots are normal as the short barrel heats up. But, when shooting from a rest, what part on the gun is sitting on the gun rest? Many people put the forestock or tube magazine on the rest. This will make the problem much worse. Marlin's group significantly better if you place the bottom on the receiver, just forward of the lever, on the rest, leaving the forestock and barrel "free-floating".
Also, if you have a micro-groove barrel, and there is the slightest bit of rust or pitting in the barrel, the shallow grooves really fill up with burned powder quickly and the groups get bad, unless you run a brush or patch through it every 5 or 6 shots. Try smoothing the barrel just a bit with JB Bore Paste. Only 3 or 4 passes, because it is an abrasive.
2. Problems with feeding. The lifters do wear out with age. Order a new one from Brownells. They are pretty easy to put in yourself. It will probably cure the problem. If not, then your rifle is really worn out and short of spending $300 on custom work, you probably won't be able to fix it.
Hope this helps.l
Mannyrock