Is it permissible to marry a woman with whom I cooperate in righteousness and piety and who reminds me of Allah, knowing that she is engaged to one of her relatives and her family refuses her marriage to an outsider, and I fear that if I leave her, she may do something to herself or regret it later?

You must immediately end your relationship with this engaged girl. Your correspondence and conversations are forbidden and a deception from Satan. It is not permissible to use religious terms to justify them. Just as you would not accept this for your sisters or daughters, do not accept it for other people's daughters. She is engaged, and the Messenger of Allah, peace and blessings be upon him, forbade proposing over another's proposal, so how about secret conversations and correspondence? Fear Allah and leave her alone, and let her family deal with her affairs. She might marry someone better for her, and one who does this cannot be trusted with a home or raising children.