That's actually incorrect. Many people believe a quantum computer may be more powerful than a classical computer, but that is definitely not proven and plenty of people also believe that may not be true.
Quantum computers are never going to replace or speed up every aspect of classical computation, but the idea of accessing them as a service for certain types of computation is probably not many decades off.
[0] https://quantumexperience.ng.bluemix.net/proxy/tutorial/full...
(Technically we still don't really know whether physics actually allows quantum computers with more than a few bits. Quantum mechanics says yes, but the universe can still veto.)
yes. What isn't proven is that actual implementation of quantum algorithms would be fast enough (i.e. while a given quantum algorithm may be order of magnitude faster using the number of steps/operations a the metric, may it happen that the runtime (using time as the metric) of those quantum steps may take order of magnitude longer ?). There is some indications that various corrections/etc. have to grow faster than linear with the number of qubits.