Loose motor mounts.
There are many reasons why your car might vibrate while it is idling. It could be running too hard for example.
It is idling. This is hard for an engine to do smoothly.
Possibly due to engine mount
Yes, when idling and driving.
As the vehicle sits idling the driveshaft is not rotating.
Probably wheel bearings or wheels are unbalanced
My guess would be to look at the motor mounts to see if they are loose or broken.
Many times when calculating miles per gallon, automotive companies will list both city mpg and highway mpg. City driving includes less miles, but more stopping and starting, and idling in traffic.
this answer is hard to find
It depends on how long you are idling, or how fast you are going. If you know you are going to be idling for a long time, it's best just to put your car in park.
It's a 1997 Tahoe