You have to also realize there are implied omissions there. We would say "anybody but him!" or "anything but that!" or the like. The nature of だけ precludes a need to actually mention the alternatives.
2. I would assume it is read で and guess that it is a countdown timer started upon leaving the airport rather than being set to go off at a specific time. Does the story give no clues?
Yes, it's from the Tatoeba site. The Tatoeba sentences are mostly OK, but there's a sprinkling of errors and bad translations. Of course, on the Japanese side I often can't tell errors from correct language that I just I don't understand.