I'll state right up front for the record I'm no expert in this. But I've been interested in the idea of using hydrogen as a motor fuel for a long time (since the late 70's), and have read-up on it a bit. I even experimented with a home made electrolysis unit a little bit at one time.
I would believe the only way to improve mileage or power in a car with hydrogen is to have the hydrogen supplied WITHOUT using the car's engine's power in any way, unless it's truly from an otherwise "wasted byproduct" (like if it's generated by a sterling engine running off the heat in the car's exhaust, or something like that). The molecular bond that holds water together is very
strong. Which means "splitting water" takes a LOT of energy (and re-combining it RELEASES a lot of energy - the Space Shuttles' main engines ran off combining hydrogen & oxygen). But there are always losses in these steps, so in a closed system (everything on-board the car), there would be a net loss.
Now, with another energy source - like solar cells on the roof - to power the hydrogen generator, you might get a net gain, but it would be small. Probably a lot better to just use the solar cells to boost the car's existing electrical system and take a bit of the load off the alternator.
To use hydrogen, and actually benefit from it, I think the water needs to be "split" elsewhere and then "loaded" onto the car as fuel. There are even difficulties with this, because hydrogen has such a low density, you can't really store a lot of it without heavy pressure tanks, heavy hydride tanks, or exotic cryogenic liquid tanks. And there's a bit of a danger element when fooling around with hydrogen, too.
Really, when you think about it, gasoline is almost a "miracle product". Just look at how cheap, lightweight, and easy to carry a gallon of gas is - and how far your car will go on it!!! Even a non-modded car. It's a tough act to follow.
So hydrogen - - - a really neat idea, but really hard to implement - unfortunately.