Is saying "I am solitary" or "I am alone" to someone who asked "Are you married?" considered a divorce, given that the speaker is married and has no intention of divorcing, and what is the ruling on repeating this statement?

Such a phrase does not result in divorce if you did not intend divorce. In Imam Malik's Muwatta, it states: "If he intended divorce by it, then she is divorced, and if he did not intend divorce by it, then she is not divorced." In Al-Buhuti's Daqa'iq Uli al-Nuha, it states: "If it was said to the husband of a woman, 'Do you have a wife?' and he said, 'No,' intending to lie, she is not divorced." Similarly, if he intended, "I do not have a wife who makes me chaste or serves me," or similar, or "I am like one who has no wife," or if he did not intend anything. However, if he intended divorce by it, then it occurs. Dealing with such questions, if you wish to conceal your marriage, could be by not answering them, or by an answer similar to yours without intending divorce, or by a general answer that achieves your objective and does not put you in an awkward position.