Can be a bent wheel, tire out of balance, or worn suspension parts.
Yes, either can cause a shake while driving.
Out of balance or damaged tire(s). Damaged wheel(s). Engine misfire. These are the three most common culprits.
Yes, it can.
Loose motor mounts.
check motor mounts
Engine mounts
Yes it will.
cause they do
If other things vibrate as well as the steering wheel you might have a damaged motor/transmission mount.
You may need rotors
It would be highly unlikely.
No,but tires out of balance will cause this. Have them balanced and rotated.