No. 1 could be the door latch - put strips of tape above and below the latch on the B pillar (to keep it in the same position vertically, as you only want to adjust it horizontally) and unfasten it moving in or out slightly until the door closes properly. I had to do this in my car recently also.

You're correct on no. 2, the door locks are vacuum operated. The pump is under the rear seat on the passenger side and if it's being lazy there may be a leak somewhere, sometimes in the door hinge where it's flexed often. The vacuum connectors can be plugged with golf tees, detach and plug the lines one at a time until you isolate the leaky line, and go from there.

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Steven Harrison

1993 300E2.8 - 196K
2001 E320 4MATIC - 86K