Is khulʿ in this case considered an irrevocable divorce, and is it permissible for the husband to take his wife back immediately by saying, "I have taken you back to my wedlock," or does it require a shaykh and witnesses?

Marriage is valid when its well-known pillars are met: the presence of the woman's guardian, two just witnesses, a dowry, and a formula indicating marriage, even if the wife is under the age of eighteen. Registration with administrative bodies is not a condition for its validity. If the state does not accept the contract before this age, the initial contract can be maintained and registered later.

If "annulling the contract" means cancelling it without a divorce from the husband, then the initial contract is valid and remains in effect, and there is no need to renew another contract.

However, if a divorce occurred before consummation or the waiting period (iddah) ended after consummation, the contract must be renewed with its pillars, and it is not a condition that it be done by a shaykh.

If consummation occurred and the waiting period has not ended, the husband may take his wife back. If "khul‘" (dissolution of marriage) means giving compensation for divorce, then the contract must be renewed with its pillars.