Nice pickups, great price. I don't know anything about the "corker" and I sort of think that is a capper, not a corker, but I might be way off base with that.
As to cleaning that carboy, fill it with fairly warm water and rinse out a few times. Then fill it, add one scoop full of oxyclean and let it sit overnight or for a full day maybe. You may need to repeat and you may need to get a drill mounted carboy cleaner to run around in there. Think carwash pom-poms for a carboy, they run about $10-15, but are almost a must have for cleaning stubborn stuff inside carboys.