LIFT OR UBER IS THE BEST WAY.
Bee-line bus service. Maps and timetables are on Westchestergov.com. Fredy is correct - it is the #12 bus line. You will need exact change - fare is $2.75, coins only. But you can use an NYC Metrocard.
I am unable to answer that question. But I do recall seeing a bus stop a few hundred feet from the entrance of the terminal.
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