Did Not vs Have Not?

Use it when you echo a question that asked "Did..." Did you see Grimm last night? No, I didn't. Use "have not" when you are talking about something that started in the past and continues to the present.

Did not have or had not?

"I did not have the intention" (simple past) refers to a specific time in the past. "I had not had the intention" (past perfect) refers to a time in the past before some other past time that has been referenced. * For example: "Until last Monday, I had not had the intention..."

When to use did not and had not?

They're both correct. You could say "he did not invite me" or "he had not invited me" in that situation. In this instance, either one would work, but that's not always the case. The latter one shows that the want of invitation had occurred before he hosted the party.