Q. Is it permitted to pick up an open fax from the office’s fax machine, to see for whom it is, since you would be reading the information of someone else?

A. See answer above in regards to e mails. Hilchos K’tanos (1: 59) prohibits the reading of a letter that was left in an unsealed open envelope. (Leket Hakemach 334, Kol Gadol 120)
However some Poskim (Chevel Nachalaso 84) maintain that faxes by their nature are sent by individuals who may not care who will read them. They compare them to post-cards on which the Aruch Hashulchan (Y.D. 334: 21) sides that there is no cherem since the sender seems not to care. (Miyam Hachalcha;2: 61, maintains that although there is no cherem on reading other people’s post-cards, one should morally abstain from doing so when not necessary).
Chasukei Chemed (Bava Basra 60b) debates if faxes are included on the cherem. He suggests that people do mind who reads them but they may not have another alternative. He remains in doubt.
Horav Shlomo Miller’s Shlit”a opinion is that if there is a cover letter, he does not need see the fax itself. If there isn’t, he should only read the address.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a