"He didn't use to ... is correct. The verb is "use" and since the auxiliary "did" requires a plain (infinitive) verb-form, "use" must be correct. "Use" has no present tense form, but the past tense form "used" occurs in examples "He used to smoke" and the odd-sounding "He usedn't to smoke" and "Used he to smoke"?

Did he use or used?

The form considered correct following did, at least in American English, is use to. Just as we say "Did he want to?" instead of "Did he wanted to?," so we say "Did he use to?" instead of "Did he used to?" Here again, only in writing does the difference become an issue.

Did not used in a sentence?

[M] [T] He didn't give me anything to eat. ... [M] [T] She didn't feel like eating lunch. [M] [T] She didn't try to evade the truth. [M] [T] She didn't want him to play poker.