Yes you can stay on either end as long as its not the last train. I can't recall cost.
Its a 30 minute stop in Rockaway. You can stay longer and wait for it to come back again as long as you didnt ride the last one out. Prices above seem correct to me
The name of the train in the online ticketing system is the "Coastal Excursion" You can return on a later train on the same day. One way fares are also available for walkup tickets only.
I think it's $22 for adults, if I remember correctly. Yes, the train stops in Rockaway for about 20 mins and then leaves back to Girabaldi. You can, of course, not get back on if you'd like to end up in Rockaway, or have a car to get back to Girabaldi or something.
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