Does the divorce take effect with the statement, "You are divorced if you throw the food," if the wife threw it in the sink and then returned it to be eaten, knowing that the intention was to threaten and that the wife was menstruating, and if it does take effect, is it the second divorce?

If the intended throwing (of the divorce pronouncement) does not occur, then the divorce does not take effect by the aforementioned throwing. For a general لفظ (utterance), the intention specifies it. Swearing an oath of divorce with the intention of threat results in divorce upon breaking the oath. Divorce pronounced during menstruation is valid.