Sounds like a misfire caused by electric supply to plugs.
Yes, when idling and driving.
A clogged muffler can.
spark plug gap Can also be a vacuum leak.
Loose motor mounts.
Yes, either can cause a shake while driving.
I don't know you tell me.
Is the car running ok? If yes and its only the vibration that's an issue most likely cause is motor mount(s)
check your powerstearing pump for fulid or belt slipping , most commond cause. hope this helps dave
bad/partially blocked catalytic converter. - kind of a rotton egg smell, right?
It might be a broken motor mount or transmission mount.
It needs an front end alinement or your tires & wheels need rotated
The "check engine" light should be illuminated. Start with investigating the code(s). They may lead you to the cause.