YourSelf, I also happen to live in Europe, and in my view immigration is a more complex issue here than in America. Adopting the American identity is easy, especially after the 2nd or 3rd generation. In Europe it's the opposite - for each generation, ethnic groups are becoming more polarized (at least psychologically). There is an American dream for everyone to be chased. There is no Dutch or Italian dream.
I agree that we have much to learn from each other. Secular Europe could learn from Islam the importance of spirituality and strong brotherhood (i.e. the concept behind the Ummah). In turn, like you say, us native Europeans could help them moderate their religious extremism. In a perfect world, there could be a good exchange.
However... I don't like to say this, because I'd love for everyone to be friends, but I'm not so optimistic about Europe's future. The sort of fatalism and lack of cultural confidence from the native Europeans, mixed with the militant attitude of immigrant youth, is a very bad sign for the continent. I have hope that we can fix it somehow, in the future. We can't create Nirvana perhaps, but we can try to soften the blow a bit. Because something has to change if we want to avert disaster.