There is uber! No shuttle. You can take a train into Manhattan which will bring you to grand central station and then you can take a bus from port authority to Newark airport. I've never heard of a shuttle from airport to airport.
Those are entirely different airports. Use a taxi service like Uber.
No shuttle if you take a taxi/Uber it'll cost you over $100 and take about two hours. You could take public transportation but that should take you at least 2.5 hours. JFK - EWR is *NOT* a good connection.
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