This is a self-exited vibration problem.
Wheel bearings are the most common for causing a vibration.
Front rotors could be warped. Replace
Your automobile may have a tire out of balance or a worn part in the front end causing this "shimmy" effect .
Your automobile may have a tire out of balance or a worn part in the front end causing this "shimmy" effect .
Tire out of balance, bent wheel, loose wheel bearing, defective tire, loose wheel lug nuts, & worn steering or suspension parts.
Tire(s) out of balance/old, bent wheel, etc.
Alignment
Or wheel and tyre.
More likely than not you have a tire out of balance or a bent wheel. Have your tires inspected and balanced.
Tires/wheels out of balance?
The steering wheel shimmering could be warped front rotors, when slowing down. The stalling when slowing down could be a bad fuel filter.
Brakes