Sounds like the "door strap" has failed. It's a ball bearing glide that provides the intermediate stops. The bearings get dirty and then they start popping out and getting sticky. Removing the door panels is only tricky if you try to force them and break off a hook clip on the inside of the panel. Luckily they can be reguled.

As for the separation of the covering . . . that's really a tough fix. Lots of people have tried all sorts of adhesives, but will varying degrees of sucess. You should keep an eye out for a decent replacement panel from a recycler or other source.