What are the matters that a Muslim girl should consider and verify when a young man proposes to her, especially if there are no Muslim relatives to inquire about him, to ensure his honesty and religiosity?

This manner of communication in daily conversation is incorrect, and you must refrain from it. Your mother should ask him to stop. If he is sincere in his desire to marry you, then he should propose to you through your guardian (wali). If you do not have a Muslim guardian, then the Muslim ruler (sultan) is your guardian. If there is no ruler, then guardianship belongs to the Muslim authority figure who is influential in your location (such as the director, imam, or khatib of the Islamic center). His suitability as a husband must be verified. To learn about the matters you should verify in a husband, please refer to question number (5524). For the conditions of a Muslim woman's guardian, please refer to questions number (6908) and (6997).