The most common causes to a problem like this is a bad motor mount, and of course, its usually the rear one that is the hardest to access.
The circumstances of the problem will help in its diagnosis.
(I'm assuming based on your title that the car is an automatic).
These are the things i would use to diagnose the problem.
1. To check on the motor mounts, you can try to shake the engine by hand (let the motor cool off a while so you don't burn yourself. If the motor rotates much front to back or side to side, you likely have a busted motor mount. Also, have a friend sit in the car with the brake applied and move the car from neutral to drive or reverse. A bad motor mount will be apparent by a much larger than normal movement of the engine.
2. If your engines RPM drop or fluctuate when you are stopped with the car in gear, it may be a vacuum related issue or related to you air conditioning. Does it happen with you Air conditioning both on and off? If only when its on, look there. You may need to service your AC compressor or belt. Your brake booster or other vacuum hoses may also be leaking, causing the engine to run roughly. You can usually see the brake booster hose is a larger black vacuum hose the goes from the brake booster on the firewall to the back on your intake manifold. You can Google all this for pictures, but if you aren't comfortable identifying these parts, you probably should get some help for the repair.
3. If it isn't one of these issues, it may be a more serious issue related either to your engine or your transmission. Engine vibrations you may not notice when the car isn't stopped, or a problem with your torque converter in your transmission could causes theses symptoms, but they would likely be more wide-spread (vibration at all times, or while driving)
I have worked on a few vehicles that have done the same thing you are explaining. It took me a while to find it but it turned out one of the engine mounts had the rubber bushing gone basically worn out. With the car in gear and your foot on the brake it puts a load on the motor causing it to bounce off the motor mount where the rubber used to be.
Master cylinder may be leaking, brake pedal may slowly fall to the floor when you are stopped with your foot on the brake.
place a latex condom over brake pedal and that should do the trick
If you have a manual gearbox you should use neutral AND foot brake at traffic lights. If you have automatic you can leave it in Drive with your foot firmly on the foot brake. (Some instructors would tell you to move it to neutral and keep your foot on the foot brake.)
If you were rear ended while you were stopped with your foot on the brake there would likely not be a 360 rotation of your vehicle tires.
Only if you want to slow down or stop, or remain stopped.
It is not a good idea to drive with two feet on an automatic transmission unless your stopped on a hill. In that case you would press the brake with your left foot and the gas just a little with your right foot.
The emergency brake release on a 2010 Chevy Malibu is located beside your left foot. You would push down on the emergency brake pedal to release it while having your right foot on the regular brake.
if a car ran over your foot would it brake because your foot has bones in it and they are very sneaative?
The brake pad squealers are warning you to have the brakes serviced soon.
Taking your foot off the brake pedal...?
You would use your right foot on the accelorater and brake. Your left foot on the clutch. If the handbrake was in the middle of the car you would use your left hand and the same with the gear lever. If the handbrake was on the door side of the driiver you would use your right hand. You would use the same foot in a British car, as you would in an American, Japanese, or any other type of car, which is of course your right foot.