Is it permissible to marry over the phone or the internet out of necessity, to avoid falling into fornication, in the event that there is no sheikh or authorized marriage official available in a very remote area?

If the woman and her guardian are present in the same village as you, it is sufficient for the guardian to say: "I give you my daughter in marriage," and for you to respond: "I accept," in the presence of two witnesses, and the marriage is valid. If the woman and her guardian are in a distant village, you can appoint someone to attend the عقد (contract) and handle the ijab (offer) and qabul (acceptance) on your behalf. However, a marriage contract via the internet or phone is not valid.