Since people increasingly live their lives online can I be yotzei the mitzvah of bikur cholim by visting the choleh's Facebook page?
You only fulfill the mitzva if you poke the sick person's page, as the well known talmudic dictum states:
Poke chazi mai ima davar
Go see what is happening
Yes, this fulfills the mitzva. As the g'mara says:
כל המבקר חולה נוטל אחד, מששים בצערו
Whoever visits a sick person washes one hand; they are feeling his pain.
Obviously this is not referring to visiting in person. As signs all over the hospital inform you, you should wash both hands when visiting in person. So it must be referring to visiting on Facebook.
Well if the fellow is virtually sick then a virtual visit would be adequate. (Hilchos Internet Perek 27)
It depends on the state of the sick person. If it's a case of Pikuach Nefesh or Sofeik PN, everything is allowed. If the person is Chole kol Gufo, he probably is in bed where he will not be able to use his PC or laptop. If it's only miktzas chole, why do you want to visit him anyway?