Is the aforementioned online relationship, which is limited to benefiting from the girl's knowledge and supporting her in religious commitment, permissible by Islamic law, and is it considered one of the necessities that permit it? Is it permissible to be reassured about her in the future after separation? Is it permissible for her to consult him as a doctor?

It is necessary to avoid acquaintanceship and conversation between men and women online due to the corrupting influences and temptations that result from it. This is not justified by calling it a relationship of brotherhood, or by seeking religious rulings, or medical consultations. There are legitimate alternatives that obviate the need for such a relationship, which leads to the Devil's snares.

Therefore, you must completely sever that relationship, seek Allah's help, and pursue knowledge through legitimate means. You can also consult and interact with beneficial Islamic websites to strengthen your commitment and provide you with useful knowledge, as there is no risk of surveillance in doing so.