A worn or loose out of adjustment drive belt could be the cause.
Usually, it is your fan belt slipping due to moister. You can get a spray for it at your local auto store.
when running acand adling tuck vibration bad
A car that is stopped with the engine running.
It sounds like you need a new serpentine fan belt.
Taking your foot off the accelerator.
Either your fan belts are going bad or your alternator is going out. If you take a bar of soap and press it against the belts while the car is running, the squealing should stop.
There are many reasons why your car might vibrate while it is idling. It could be running too hard for example.
Yes, "sparkling plugs" is definitely detrimental to idling or smooth running of an engine
Check the condition of the accessory drive serpentine belt, belt idler pulley and belt tensioner pulley bearings.
Could be,in need of a tune up, a vacuum leak, contaminated fuel (water), If we knew what year, make, model and engine more info would be available.
Idling is what your car is doing when it is just sitting somewhere running. As soon as you press on the gas it is no longer idling. Your idle speed is the number of RPMs your engine runs at when you are idling.
Probably wheel bearings or wheels are unbalanced