I wanted to finalize this thread with two things:
After reconnecting the vacuum connections that came loose, I felt some jerkiness in the transmission. But this was temporary. Somehow it righted itself after driving around a few times. I assume there is no leak anymore.

The humming I was hearing was the antenna. I just had to turn the switch off.

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1985 300d Turbo, 274k miles
my first and only car