Obviously the vacuum shutoff is not functioning at the key and this may be due to multiple vacuum leaks in your systems. The brown vacuum lines are the ones that control the shutoff function, one to the key ignition switch and one back to the back of the IP.
If you get a small vacuum tester it will pay for itself indiagnosing lots of stuff on these cars.
You can try disconnecting and plugging off vacuum lines but as leathermang stated if the vacuum pump is blown then your source is at fault and you have no vacuum to use for shutoff...

The manual shutoff problem could just be casued by a bad or worn idle adjuster. This is on the engine block side of the IP and has a spring loaded tip that sits on the idle control arm. You adjust the idle by loosening the locknut and then turning the bolt with a screwdriver. That is assuming that the idle knob cable from the dash is adjusted correctly.
Anyway, on my 1980 the spring in the adjuster was weak and partially compressed. This meant that I couldn't compress it enough to kill the motor just slow it way down. I replaced this part with a used one for a buck and it works great now...

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'99 S420 - Mommies
'72 280SE 4.5 - looking to breathe life into it
'84 300SD Grey - Sold
'85 300SD Silver - Sold
'78 Ski Nautique