Most common cause is warped rotors.
There are a small number of things that can cause the steering wheel to shake, and none of them are anything to ignore. A bent rim, a damaged tire, a loose tie rod end, and at a minimum - an imbalanced tire/wheel. You need to have this checked at a garage.
some cars yes (like 4 drive)
A worn or damaged component. Suggest to have someone wiggle the steering back and forth while you inspect for excessive play.
Power steering box... Steering fluid level low,dirty or needs replacing... If power steering fluid is white then your box is damaged...
Bad mount on the steers, worn/loose/damaged steering components, axles out of alignment.
That is typically a wheel balance problem.
It doesn't. Your face will be less damaged hitting the airbag than if it hits the steering wheel.
Steering fluid leak.
If they are warped they can cause shaking when braking.
the most likely cause of that would be the power steering pump failing.
A shaking steering wheel means something is wrong. Can be a tire out of balance, bent wheel, or suspension problem. Whatever it is, the shaking it putting stress on other parts and can cause other things to wear out. It is especially hard on wheel bearings. have this diagnosed and repaired asap.