89 300E Shake after start

I have a 1989 300E with 710,000km and lately after I start the car the car shakes as if it wants to die. Sometimes it dies and sometimes it does not. While driving the car is great but when I come to a stop it shakes again. This happens for the first 5 minutes after starting the car.

On a seperate note when the car is on there is a load hum sound coming from the passenger side dash. I have no idea what it could be. This sound is on all the time.

Also some of the factory stereo light are burnt out. Is there anyway I can replace these light bulbs and if so how would I remove the stereo.

Thanks for all your help

Fab