5,000 PSI for the Honda. For reference, scuba tanks go over 3,000 PSI. Other hydrogen tanks go up to 10,000. Extensive testing has shown it to be quite safe.
Why not grow a fuel that is energy dense and easy to work with at room temperature, such as oil?
Because current methods to turn it into useful work are extremely inefficient and prone to breaking down. The fuel cell in that Honda is about three times as efficient as the average engine and has almost no moving parts except for the electric motors.
Like I said, there are different issues. One is where the power come from: renewable, nuke, algae-grown oil, etc. The other question is the best portable power source to make our cars run.
Gasoline is one way to store hydrogen. There is 64% more hydrogen in a gallon of gasoline than a gallon of pure liquid hydrogen. The inefficiency of compressing hydrogen negate the efficiency of burning it later in a fuel cell. With all its special handling requirements I just don't see pure H2 becoming a mainstream transportation fuel.