Yes the mushroom goes inside the post, its a good idea to clean up all the parts when you have it apart, I find a soft stainless brush from a coffee machine cleaning kit works the best, for years things like that were expensive and hard to find and I used a brass swede brush from a shoe shop, a pot scrubber does a fair enough job.
As for the "odd little seal" I would have pulled down hundreds, possibly thousands kegs and have never seen one. There were lots of variations and special purpose kegs out there, some have odd shapes to the fittings and the parts welded to the keg but what you are describing is new to me.
My first thought would be that someone has added a non-return valve for some reason. I would love a picture, its always good to learn.