I found the pumpkin, the companion flange is still in place. It would probably just need fluid to be ready to go.
That guys picture is of an open differential, and some bearings. Is he trying to troubleshoot some of you problems by saying that will fix it? I'm betting some bearings are bad or are going bad if you're hearing a humming noise while idling down. Bad thing is the costs to replace the bearings is expensive. I just replaced most of my bearings and my final drive since it was damaged (scratch on one of the grooves) parts and labor was near 900 dollars 3 something of that was the final drive ring and pinion.