Do truck drivers take the DOT drug and alcohol tests?

The drug test is a random test.
I have taken it as part of my DOT physical, and sometimes I haven't.
As part of the physical itself, no its not required.
However, if your company demands it, then you take it.

The drug and alcohol tests are random, and can be given any time for any reason.

As a CDL holder you should know this already.

BTW, I held a CDL for 25 years

I worked for an oil & gas service company. Our CDL drivers went through drug testing as part of the hiring process, at random, and for cause during their period of employment. A refusal (balk) was counted as a failure.

And yes, as a CDL holder, one would already know this.