Technically, a Class B, but employers will probably expect you to have a Class A, plus substantial open deck experience. You'll be expected to run one of the trucks and flatbed trailers if need be.
A mobile crane, like the kind you see going down the highway? Yes. Absolutely.
Yes, you will need insurance to drive with a CDL license.
You can operate the crane - you just can't drive it down the road.
It depends on the model. You need a CDL to drive one that bends in the middle or is over a certain length
If the vehicle requires a CDL in service, it'll require a CDL for the test drive.
Yes you do need a CDL License to drive a bucket truck.
No
no
Vehicles which are not used for on-road use do not require a CDL.
No
No, just to drive it.
If it's a truck which anyone else would be required to have a CDL to drive, then yes.