What is the ruling on the current relationship with the girl online? Is it permissible to marry her without her Islam being proven in court to avoid problems? Is it permissible to be associated with her without her family's knowledge, and what problems does that entail? Are there any religious impediments to marrying her because she has embraced Islam and wishes to live in a Muslim household?

Marrying a Muslim woman who recently converted from among the People of the Book contains great good for her and for her husband. Governmental departments are not required to prove her Islam. It is not permissible for her non-Muslim father or relatives to solemnize her marriage contract; rather, a Muslim judge should do so. As for your relationship with her before marriage, she is a stranger to you, and your relationship with her must be cautious and only to the extent of need. It is preferable that you seek a Muslim woman to assist her. In conclusion, there is no impediment to your marriage with her, legally, if the pillars are fulfilled, and her guardian is the ruler if she has no Muslim guardian.