What is the religious ruling regarding a man divorcing his wife by saying, "I swear by divorce that you will travel to your country," and repeating that with the intention of threatening her, then saying to her: "Give me a paper so I can write for you that you are divorced," without actually writing it? And does the divorce occur while she is menstruating?

You mentioned that you swore an oath of divorce upon your wife for her to travel to her country, and she complied and traveled. Therefore, nothing is incumbent upon your oath, and no divorce occurs thereby.

As for what happened during the quarrel, and your saying to your wife: "Give me a paper and I will write for you that you are divorced," nothing is incumbent upon it, because you did not intend these words. Rather, they came out of you by mistake, and your intention was to write to her that you would divorce her. This falls under the issue of the divorce of one who errs and did not intend to utter the word of divorce but his tongue slipped to it, so nothing is incumbent upon him.