No, you do not.
To operate ANY vehicle which requires a CDL of ANY class in ALL states (this is federal law - it doesn't vary by state), the driver must have, along with the appropriate class of CDL (A, B, C), a DOT Medical Card. However, this is assuming you're were referring to a Class C CDL - several states issue a non-CDL Class C licence.
You will need a Class B CDL with tanker endorsement.
Class 3 truck with a rollback body? No, it doesn't require a CDL.
No. The weight determines what class licence you must obtain (there are non-CDL Class A and B licences available), and the usage is what determines whether or not you actually need a CDL class licence to operate it.
You will need a Comercial Class Drivers License. This is usually a Class A CDL in most States. So you will need CDL training.
You would need a Class A CDL for Dump Truck. It's not as intense as more restrictive classes of CDL.
Yes. Always.
Yes, you would. Without the trailer, you could operate it with either a Class A or Class B CDL.
Depends. You can drive up to a Class 6 truck (up to 26,000 lbs. GVWR) without a CDL. Class 7 or Class 8 trucks require a CDL.
Yes. In most cases you will need a CDL Class B license because of the weight of the truck. However, if you would be driving a semi with a dump trailer, you would need a CDL Class A license.
Depends on what class of CDL you're going for, among other things.
Yes. You can drive that vehicle with either a Class B or Class A CDL.