Visiting Europe is wonderful. Sure you'll have a great time.
The passenger mix in Europe will be different from the Caribbean. You'll see many more Europeans onboard, but the bulk is likely to still be American.
The ship will exchange dollars for Euros onboard, but I certainly wouldn't recommend using their service. They charge quite a bit more on their exchange rate. I'd simply use ATMs in ports of call, and credit cards for larger purchases.
The US dollar is the currency onboard, and in the casino, regardless of where the ship is.