Is the waiting period (iddah) required in this case, and what is its duration, and is it permissible to take her back during it with or without her knowledge?

If the marriage contract was handled by an authorized representative from the Islamic Center, then the contract is valid and does not require renewal. However, if the representative was not authorized, then the contract must be renewed through your guardian (wali) or his agent. You are not required to observe an 'iddah (waiting period) if the husband is the same person. The man who married you in an invalid marriage cannot reconcile with you except through a new contract and a new mahr (dower).