A watch not worth a penny was being sold there.
In this sentence, do I have to, must and should put "that is" like this?
A watch that is not worth a penny was being sold there.
No, you don't have to include "that is". However, if you do want to, it should say ...that was... so that it agrees with the rest of the sentence.
You would use "is" if the sentence were in the present tense, i.e. ...is being sold there.