India itself is more diverse than EU. Ethnically, culturally, linguistically. If you think it's such a great achievement to have a federation of similar countries, how much more awesome is it for 1.2 billion very diverse people speaking 30+ languages and hundreds of dialects living together as a single country?
As for the NATO - it is mostly the USA's muscle that holds it together, and the contribution of Italy is negligibly small. Besides, we saw just how much NATO could do when Russia took Crimea away. European countries can't do anything militarily, without riding on the coattails of the US military machine. The whole NATO thing is just an excuse for USA to have bases across the world. Without the American military, NATO wouldn't exist. Without any other military, say German or Italian, NATO will still exist.
Not really. Until the mid 20th century, they were still killing each other senselessly. How many Europeans killed aech other in WW2? It was only after that event, that they learned to live together in peace. (Which they have done quite well.) Compared to that, India and China have had one border conflict in the past 5000 years or so. Europeans are really in no position to teach us the glories of peace.