Nobody knows the correct answer to this. Many things would have to happen, but any answer to this question would be essentially speculative. You can make up almost anything you like. Primarily, oil use would have to become much more expensive.
There are still some major problems to be overcome with hydrogen fuel cell technology. Ion exchange membranes are not perfected; waste water clogging and removal from the membrane surface is currently not well understood or solved; and storage and distribution of hydrogen has not been solved. It's impossible to answer your last question as both are probably true.
Most energy experts would likely agree that the first and most important step is to make oil less popular, either by decreasing the supply or raising the price. But since too many people are making too much money pumping oil out of the ground and selling it, this is not about to happen for another ten or twenty years, or maybe more. Until then, there is not much monetary incentive to work on alternative energy sources.