I thought that zou + moeten is 'should'? How would you say "no, i did not have to do that"?
"Ik hoefde dat niet te doen" or "ik heb dat niet gehoeven te doen", sth like this, i guess?
That combination of tenses doesn't work. You could say "Dat zou ik niet moeten hebben gedaan", which is grammatically correct, but sounds a little awkward to me.
This is a modal Pluperfect rather than Perfect, or no? Just checking.
no - must can only be used like this:
I must do this. I must not do this. I must have done this. I must have done this.
However - "I must not have done that" - translates differently - like if you were saying, "in hindsight, I thought I sent the check, but since the check never arrived, I must not have done that."
"I should not have done that" is a better translation for what they're going for here...
Hope that helps! These helper verbs in English are pretty nuanced.