Does divorce take effect if a man says to his wife, "If you want me to divorce you, I will divorce you," or "After you menstruate and become pure, I will divorce you," with the intention of not causing a divorce and merely gaining time?

A woman is not permitted to seek divorce without a شرعي (religiously valid) excuse, due to the severe warning mentioned concerning it. The husband's utterances, such as "I will divorce you" or "I divorce you," are merely a promise of future divorce and do not constitute a divorce unless he intends to effectuate the divorce immediately.