Is it permissible for me to use the Internet in a way that pleases Allah after I swore an oath on the Holy Quran that I would not use it except in the presence of a person who threatened me if I used it incorrectly, especially since I do not wish to be associated with that person?

The use of the Internet is fraught with dangers, and it should be avoided if other means can suffice, because nothing equals safety. As for swearing by the Mus'haf (Qur'an), it is a binding oath that necessitates expiation if one breaks it. Placing one's hand on the Mus'haf or opening it in front of the swearer does not increase the severity of the expiation.