I will not answer if you got the CDL question right till others answer.
But for the DOT#. It depends on what state you live in.
If you cross a state line with the truck then you need one in every state.
If your main office is in one state (lets say Va) but you work out of a differant office (lets say N.C.) then you will need it even if you do not cross state lines.
Both of these really do not apply to most plumbers.
But if you live in a green state you need one even if you do not cross state lines.
This is what brings up very big up risings.
Some green states have exemptions to the rule for some people. Some try to say if he has a exemption why not me. We have the same size truck.
Or the state may try to do away with a exemption. This happened in Iowa a while back with farmers. There was a bunch of stink to finelly the state backed down.