Can I mentor from a distance?
I understand that sometimes you are acquainted with a younger believer who lives far away from you. Paul clearly mentored Timothy even when Timothy was no longer in Paul's presence. It's biblically acceptable, and I would say that it's logistically possible as well, particularly because of modern technology. In fact, I have mentored young Christians from a distance myself. It is never the best option, mind you, and I do my best to help my young protégés find someone in their local area to fall under for guidance, but it can be done.
It will be very important for your protégé to find other methods of accountability because you will honestly not be close enough to him/her to really ascertain whether he/she is meeting all of the goals you set down at the beginning of the relationship. Your protégé may tell you that the Bible reading and prayer times are good to go, but that doesn't make it necessarily so. It will be, to a large degree, up to them to make that happen. You are there for guidance, not for accountability.