Is the marriage considered valid if it took place between a Muslim man and a Christian woman (not a virgin) residing illegally, and the marriage was conducted verbally with the consent of the wife's family via phone, without official documentation, but with the intention of documenting it later?

It is strange for a Muslim to undertake an action about which they doubt its permissibility, and then ask about its ruling after having committed it. The obligation is to ask before the action, in accordance with the Almighty’s saying: {So ask the people of the message if you do not know}. Your marriage to this woman is invalid because it was without a guardian (wali) or witnesses, and her guardian's consent via phone is insufficient. Therefore, you must separate from her immediately.