AFAIK, the '95 E300D does not have a factory remote lock unless one was available for a high-end W124 E-class (like the E/500/E) and it was added as an option or retrofitted by a subsequent owner. I added my own remote lock using one of the inexpensive modules available from various Internet sellers.
The doors should not lock on their own, either when you shut them or when the car reaches some road speed; perhaps your convenience module (under the rear seat, left side) is mis-behaving. Another possibility, someone else installed a remote lock and it is doing the locking.
Inability to normally operate the driver's door lock may be a problem with that lock mechanism and/or switch. There is an electrical switch as well as a pneumatic actuator, all interlinked.
Jeremy
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"Buster" in the '95
Our all-Diesel family
1996 E300D (W210) . .338,000 miles
Wife's car
2005 E320 CDI . . 113,000 miles
My car
Santa Rosa population 176,762 (2022)
Total. . . . . . . . . . . . 627,762
"Oh lord won't you buy me a Mercedes Benz."
-- Janis Joplin, October 1, 1970