Possibly a broken motor mount. If it runs good otherwise one cause can be a vacuum leak. The check engine light should be on if it is a vacuum leak.
For the brakes, check for warped rotors. For the turning, check for worn CV joints.
Bikes with coaster brakes are stopped by pedaling backward, while hand brakes are operated by squeezing levers on the handlebars. Coaster brakes are simpler to use but may cause skidding. Hand brakes offer more control and are better for beginners learning to ride safely.
Yes, either can cause a shake while driving.
Brakes
rubber bushings in motor mount worn
Perhaps an out of balance wheel. If this is the cause it will be worse at a certain speed.
if you car shakes when its fully stopped it may be the harmonic balancer, take it to a garage. is it shakes only when you are braking while stopping than have you brakes checked
Brakes.
Bad tires or out of balance tires or driveshafts. Have it checked out.
The brakes are the primary cause of stopping a car whilst driving.
Not to my knowledge, they only vibrate if they are heated
Possibly bad wheel bearing.