The easiest was to get cash is to just use ATM's. Not many stores or shops in Europe will accept Travelers Checks, but they will accept CC's. Usually the purser's desk onboard will cash the checks, but the exchange rates are in their favor and I've heard of them running out.
A lot of places don't take Am. Express travelers checks anymore. They are a bit antiquated. ATMs are by far the best bet. Just make sure you have a 4 digit PIN that uses only numbers (not letters; some ATMs don't have letters on the numbers like we do in the US).
Yes, they will exchange small amounts of USD to Euros. The rates in the airports are usually terrible! The rates on the ship are decent, but ATMs are still a better deal.
Yes, it's a good idea, although most banks won't make a note of it. CitiGroup will though.
ATM rates are the best. Credit cards are the next best, but call each of your credit cards and find out which one has the lowest CONVERSION RATE. It may take talking to a few different reps. at each credit card company because many of them don't know what that is.
Usually, the bank will charge between 1% to 3% of the amount you charge for the conversion to USD. I found that my Target Visa had the best rate of only 1%! That card IS good for something after all. :grin
The safest thing to do is to get smaller amounts out vs. one or two big withdrawels. You can exchange any money you don't use either on the ship or in the airport, but the airport typically has terrible rates and they charge a service fee too.