The phrase "didn't used to" as a negation of "used to" is pretty common in informal English but will also be regarded as ungrammatical by many, especially in writing. There's some pretty good discussion of more acceptable ways to phrase this construction here:
When spoken aloud, "used to" will sound indistinguishable from "use to" for many English speakers.
Actually, "didn't use to" is common in American English, and one shouldn't avoid it at all. If you don't use it, then you're stuck with some formal phrase like, "I formerly didn't" or some awkward phrase like "Before, I didn't..." which is somewhat ambiguous as to the number of times you didn't do something.
"I didn't use to..." is extremely useful in colloquial English, and it's use should be encourage.
On the other hand, "didn't used to" is a double past tense form which just isn't seen in English. You don't say "I didn't gone" you say "I didn't go", "I didn't want" not "I didn't wanted".
"I didn't used to" is bad English.
"Didn't use to" is the correct version. "Didn't used to" is not, although there are some regions which accept it. "Did not used to" piles one past tense on another, and that's not done in English. You say, "I did not go" not "I did not gone" - and "Did not used to" is the exact equivalent of "Did not gone".
No, that's an entirely different verb, meaning "I am not familiar with" "I am not inured to" "I have not become comfortable with". I has nothing to do with some regular pattern of behavior, which "I didn't use to" indicates - I didn't do it in the past, but now I do it.