Disclaimer, Dutch living in Finland
1) Absolutely. It was amazing to see thousands of people all over Europe line up, sometimes in the freezing cold, in the first minutes of 2002 to get their first Euro notes. While the money is maybe not as a colorful as some European notes used to be, I like them very much. Europe has always made the best (quality wise, design wise and security wise) bank notes and the Euro is the a combination of all that experience. See also answer number 2.
2) It does of course. But the thing is *every* member of the Eurozone went along. The Greek gave up their historic Drachma's, the Germans their very stable DM and Bundesbank, France their beautiful francs, Holland their colorful guilders, Finland their pretty marks, etc. They all did this to continue with a united single currency. These are big sacrifices for any country, and they all went along and did it. This is a good moment to be very proud if you are living in one of these countries. And hey, Paris is still Paris, I just won't get ripped off when I'm there anymore :-)
Before I go on to number 3, let's deal with some misconceptions. People say it's impossible to have an economic policy for a group of economies so diversified in every aspect as the countries currently in the Eurozone. Like some other people have pointed out, it's the same in the US, different states would ideally require different policies. What less people have pointed out is that for the last 10 years (Euro was drafted at the Maastricht treaty in Holland in 1991) the economies of Europe have been brought to within less than 10% of the tolerances allowed between the states of the USA in the areas needed for the Euro to work as planned. Italy by 1997 had done so much work on their budget they are now a great teamplayer in the Euro.
Also, it always amazes me when a supposedly "real" news agency (BBC) comes up with absurd things (war on terrorism, and now the euro), and I can quote them saying at some point (website I think) .. british don't want their economy controlled by a bunch of unelected Germans .. excuse me ??? The main office of the European Bank is in Frankfurt, which given that the DM has always been the most stable currency and Germany's economy the biggest is pretty fair. Furthermore, there is a president from a different country, currently a Dutchman, to be followed by a Frenchman, etc. Germany is not "in charge" of the Euro, the Euro countries are. Unlike what the Sun tells you adopting the Euro does not mean giving up your independence. But where you could previously mask some symptoms by juggling with exchange rates et al, you are now forced to deal with the actual disease. With help from all the other Eurozone countries. Fair deal?
3) Eventually, yes. Some oil-producing Arab countries not particularly fond of the USA have already said they would want nothing more than the Euro to prove stable (which it has so far, 30% against USD doesn't mean anything and is perfectly explainable, but that's another thread) and start pricing barrels of oil in Euro's, not dollars. Europe has more people, and simply by numbers the Euro will have many more people behind it than the dollar.
First and foremost, the Euro is political, a lesson from the world wars. I have full confidence it will exceed expectations.