What is the ruling on the iddah (waiting period) for a woman who sought divorce from her husband who is mentally ill and sexually incapacitated? And is the iddah determined by the passage of time while I am with my family, or by one menstrual cycle on the basis that it is a فسخ (annulment) due to a defect, or by three menstrual cycles on the basis that it is a طلاق (divorce)?

If the husband is impotent (عنينًا - 'aneen') and has not consummated the marriage even once, the wife has the right to request annulment of the marriage (faskh al-nikah). The judge will postpone the matter for a lunar year; if he does not consummate the marriage within that period, she has the right to annulment. This annulment is not counted as one of the permissible divorces (talaqat), and the wife must observe the 'iddah (waiting period). If the husband has consummated the marriage even once, he is not considered impotent. If the wife is harmed by a subsequent weakness, she has the right to request divorce (talaq) or khul' (divorce initiated by the wife in exchange for compensation). It is recommended to use ruqyah shari'ah (Islamic exorcism/healing) as the inability might be due to magic (sihr), jinn possession (mass), or the evil eye ('ayn).