How can a Christian maid from the "Christina" sect be persuaded to embrace Islam, especially since she says: "There is no difference between a Muslim and a 'Christinian,' for we all acknowledge the existence of God"?

To thank you for your eagerness to guide that woman, you should not mix with her excessively. Your call to her should be through your wife or some of your mahram (unmarriageable kin) to close the door to fitna (temptation/strife). The invitation to the woman should be by clarifying the proofs of the truthfulness of the Messenger of Allah, peace and blessings be upon him, and the validity of his message, and that he is truly the Messenger of Allah. This can be done through the miraculous Qur’an, his praiseworthy biography and morals, and his tangible miracles. Explain to her the virtues of Islam and its superiority over all other religions, and that it is the complete religion that Allah has approved. Clarify for her the virtues of Islam in creed (aqeeda), worship (ibadah), dealings (mu'amalat), and morals (akhlaq). Strive in supplicating for her guidance, for guidance is in the hand of Allah.