No not that I'm aware of
No there is not. However there are private shuttle companies that will take you from Philadelphia to JFK. You find a few through a Google search. They're not the most professional, but they will save you the hassle of having to transfer between several buses, trains, and cabs.
I would call cause they may have added some for the holidays
No. Port authority only. But you can get there by the subway from Port authority.
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