I have Ford Focus 203. From the past few days I find the car starts vibrating when I stop in a signal with gear in D position and the heater on. Sometimes the engine shuts off as well. To know the reason I did an experiment today. I started the engine and kept it one for 10 minutes. During this time the car was not vibrating. The moment I put on the heater, the car started vibrating. Again when I switched off the heater, the vibration was gone. Can someone tell me the reason for the vibration?

One reason is that the engine may be running rough. Heaters and other devices can be hooked to the vacum on your engine manifold. If you have a leak somewhere then your drawing in extra air and that can caus this condition.

When you turn on the Electronic Air Temperature Control (EATC), the air conditioner often runs at the same time the heater is going. It does this to dehumidify warm, moist air, which will fog up your windows. The vibration is due to the air conditioner compressor coming on.

Replace the platinum spark plugs, with the same Motorcraft plugs that came in the engine, if they have not been changed in 45,000 miles. It sounds like your engine's ignition system is weak. I would also change the fuel filter and the air filter, if they have not been replaced in 30,000 miles.