This response isn't accurate, because the entire Northeast Corridor are all reserved trains.

To answer your questions:

1). If you book online (which is easiest) you will immediately get an e-ticket with a QR code that the conductor will scan.

2). You can switch to another train by changing your reservation at any time, assuming seats are available. However Amtrak prices this route in fare buckets, and as the train fills the price goes up. So you would likely be forced to pay a higher price for a different train at the last minute.

3). If you do change trains you will get a new e-mail and e-ticket. You can board the train with your old e-ticket printout and show the email on your phone if anyone asks. For that matter, all you really need to do is pull up the email on your smartphone. If you use the Amtrak iPhone app to book your original reservation it is very easy to change the reservation via the app, and you can also add the eticket to the Apple Passbook if you want.

4). I agree with the suggestion on take ground transportation from JFK. You will be fighting traffic from JFK to get to Penn Station, why not just take the suggested limo, or do a one way car rental and not waste time. The time you sit in traffic on I-95 is probably a wash between getting to Penn, waiting for train, etc.