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You can on island cruises so you can probably do it on other ships ask travel company you booked your cruise with hope I've been of some hel.
Yes see the Purser.
On all ships we have been on, Princes, celebrity, RCI, we have settled part of our account on board, in $ cash,(only because we had excess $s left over & didn't want to take it home with us), so I would imagine that you could pay it all. I presume you mean $s, the rate of exchange if you pay the $ account in £s will not be very good.