A car's steering wheel will vibrate when driving if the car's alignment needs to be adjusted.
I have the same problem with my '91 Dodge Caravan -- it is probably the transmission.
This is probably due to worn brake rotors on the brakes, if there is no vibration when driving then this will be the cause.
get a wheel alignment
It is the engine that is vibrating and it is just being felt in the steering wheel. Can be a vacuum leak, or miss in the engine.
the motor mount is bad
Normally it is a tire out of balance. Can also be a bent wheel.
A steering wheel that is padded with leather for comforment when driving
If the steering wheel is loose while driving the steering rack may be going bad. A bad steering rack leads to a lot of play on the actual wheel.
You possibly have warped brake rotors on the front. Or Bad Wheel Bearings.
Normally this is caused by a tire out of balance or a bent wheel.
yes
could be a blockage in your fuel lines.