It's an interesting idea. Unfortunately it will always take more energy to split the water molecules than you get back from burning its components (which simply remakes water).
It just doesnt add up. In the first video he has a jar which couldn't hold more than a litre of water which he claims needs topping up once a week or so. Say he used the whole jar every day (which would need about 20 standard alternators strapped to your engine to power) thats 1kg of H2O. H is 1, Oxygen 8, this means there is 200grams of Hydrogen reclaimed. Hydrogen has roughly 3 times the energy density of unleaded petrol, so this is like adding 0.7 litres of fuel to your tank that day (since fuel weighs less than water). Since his system is drawing 3.5 amps, it would probably take a month to go through a litre of water, meaning hes adding about 20 mils of "free" petrol per day. Considering that 20 mils prob only took an extra 40mils of petrol burnt to turn the alternator harder to make it, its not that sweet a deal.
If you want to play with a browns gas generator for fun, or to blow stuff up, or to learn some chemistry, go for it. If youre doing it to improve the efficiency of your vehicle, save your money for a plug-in hybrid.
First 3 videos are selling something. Last one is a really nicely engineered cell. No matter how nice your cell is conservation of energy still applies I'm afraid.