#2 and #3 Google is so influential that it's highly unlikely to happen on the current playfield. They either buy a potential competitor out or cripple their business. I can only see two opportunities for this: a) specialized niche search, b) search based on a new disruptive technology.
It's a fool's errand to try to beat Google at the game they've perfected and were built for. By the time you could very slowly wrest control of search from Google, the whole tech world will have changed and your point of competition will no longer matter. That's the foolishness of Bing, for example. It's great that companies still try to compete with them, but all they will accomplish is to keep making Google better (and that's a good thing for consumers); they won't 'beat' them however under any circumstances.
Google will be beat in search the same way Microsoft was in operating systems: a dramatic sea shift in technology (with Android now being by far the most important operating system going forward).
#2 Google has so many popular products (search, gmail, youtube, maps) that it makes sense that they're that big. It's equivalent to a person having a bank account with $1bil in it. Just leaving that money in the account and raking interest, you just continue to get bigger by being. In google's case, there isn't strong enough competition to stop them from "being" and gaining more share based on their prior efforts.
#3 Could a new US based search engine compete with Google? Or are they just that big that the task is a fool's errand?