The first two symptoms bring to mind a common 420SEL ailment.
That is the open line to the vacuum modulator. To see this one must remove the aircleaner and look down the center of the rear of the motor. From an area close to the origine of the large vacuum booster source line, there will be a metal nipple (pretty hard to see). Look for the small line going to the trans modulator, it will just be hanging there.
The leak is small but it all goes in one intake runner and kills the cylinder at idle.
There could be lots of different problems and any that reduce vacuum will affect the trans shift but the line I mention is a fairly common occurance.
Bosch Master, ASE Master, L1
33 years MB technician