Gearbox
I did a little looking at a couple of newer machine manuals I have, here's what I think you're going to have to do to fix it.
2 bolts on either end of the housing are holding a bearing with a short sleeve on the ends of the auger rakes, they have to come off. The pulley has to come off then the whole thing should slide out. Then pull the pins, and if they aren't rusted on the rakes should come off the auger shaft. Now you can unbolt the auger gearcase halves and pull it apart. Watch the bushings and seals when taking it apart. Check them over and replacing them is now a good time. If you have to replace the seal or bushing on the impeller shaft, removing the roll pins and pulling the impeller was easier for me. Take pictures as you go along.
Replace whatever is needed then reassemble.
Me, I'd check the bolts on the case to insure they are tight (don't overtorque or you could break them or strip out the holes) along with replacing the oil you have with new 30 wt as yours is too thin IMO. Try it and see if it's sealed up or not. You can always tear it down any time but it's not fun to do if you don't have to.
Good luck
PS - here's one that I had to rebuild that was packed with grease. The bushings and seals were shot in it.
