Is it permissible to initiate a discussion about Islam with a Christian with the intention of guiding them [to Islam], and not for personal gain?

You must first comply with the command of Islam yourself. Therefore, cutting off your relationship with this man is obligatory, because a Muslim does not befriend one who opposes Allah and His Messenger, and because your relationship with him as a Muslim woman is impermissible. Do not try to invite him to Islam directly. If he converts to Islam, then there is no harm in marrying him, knowing that it is neither permissible nor valid for a Muslim woman to marry a non-Muslim.