Here's what I understand, it is by no means certain as with all things.
Precisely what the situation is with the pool I don't know but from what I understand I would expect more recruitment to happen again for this year. If not, just to stand still we will need to recruit annually. Keep an eye on the Kura Linked In page for updates.
European reg aircraft do go to the US to help out with their peak times, as with all aircraft and cabotage rules they can only help out with international flights. The pilots on these aircraft have to hold and EASA licence and work for NJE.
I think this has been a fairly long running thing and I don't believe it has anything to do with retention issues over there, I don't know what the situation is and hope that our colleagues in the US get a favourable deal from negotiations.
It would be unusual for someone to have a green card and the right to live and work in the EU/UK (plus both licences) and I think there may be a couple of colleagues who have worked in both but I can't say for sure. Flip flopping between the two would be really hard I imagine if not close to impossible. That said if you can work in the US and have an FAA licence NJ inc are hiring!