What is the ruling on a Muslim girl – a recent convert to Islam – remaining in the home of her non-Muslim parents, given that they compel her to attend Christian rituals and threaten her with expulsion and cutting off her means of livelihood and medical treatment, and what is her path to salvation in this situation?

If the situation is as you described, then the girl must adhere to her Islam and not obey her family in words and actions of disbelief (kufr), except in extreme necessity if she fears perishing. In such a case, it is permissible for her to comply with them only to the extent of the necessity, while rejecting it in her heart. She must strive to find a stratagem to leave and flee with her religion. You should take the initiative to marry her and bring her to you to extricate her from this predicament.