I believe it usually uses fossil fuel feedstock but doesn't have to.
I can't see how burning hydrogen in an engine will compete though, as an electric car is mechanically simpler than a car with an internal combustion engine. As economies of scale build, cars powered by electric motors will undercut internal combustion engines in price and reliability.
No matter how refined the manufacture of electric cars gets, a hybrid will always reduce the battery capacity needed to a fraction of what it would be otherwise. I believe the typical difference between a plug-in hybrid and full electric is around an order of magnitude.
It is just as irrational to have a battery with a 300 mile capacity as it is to have a gas engine with 300 hp. In either case, you are allowing for the greatest possible need which happens rarely if at all. A hybrid allows you to build both the engine and the battery for the average case which is on the order of 10% of the worst case. This is a huge inherent benefit.
The engines are not the hard part of the hydrogen car.