Will hydrogen replace oil to run our vehicles? If so, how long?

I really don't think so. Even if hydrogen fuel cells could be made with only cheap materials rather than the expensive metals modern fuel cells use certain chemical properties can't be overcome as easily.

Per liter hydrogen doesn't even come close to the same energy density as diesel or gasoline.  In order to compensate for this hydrogen needs to be compressed to get more gas in the same amount of volume which makes it potentially more explosive. Hydrogen is also very flammable and one of the most reactive chemical elements posing possible dangers in an accident.

Hydrogen is the smallest atom on the periodic table so it eventually leaks out of most containers given enough time. It also can't be sent through pipelines as easily as liquid fuel.

Hydrogen is more of a way to transfer power rather than being a source of stored energy.  To get hydrogen you need to break chemical bonds which requires energy. Even if the energy to break the chemical bonds is harvested from solar power it really makes more sense to use the solar power directly as an energy source.