There is one certainty, the water4gas website (in the OP) and DIY kit that they sell instructions for is a complete waste of time. If you look at the kit it is made from a peanut butter jar, and a flimsy piece of copper winding!
However, there are few die hard geezers on youtube who make some really good quality hydrogen fuel cells for their own cars, and report some fuel savings. of about 20%
I am well aware of the "in thoery it is against the laws of physics" views that some people hold on the subject, but I do think it is worth having a bit of fun with the idea to see if there are any gains to be had. You will need a fair amount of money for the stainless steel plates, and a workshop, and a fair amount of engineering knowledge to do this.
Another option is the (original) Cornish hydrogen generator. I say 'original' because some idiots have usurped the name "cornish" just to sell some useless peanut butter jar type hydrogen generator plans. The usurpers can be found here
The original Cornish generator was designed by Professor F. P. Cornish of a British University back in the 80s. Based on a welding wire feeding mechanism, he fed aluminium wire at slow speed towards an electrified steel drum submerged in water, as the wire got to about 1 or 2 mm from the drum the spark between the two, was very localised and therefore did not require much energy, but the hydrogen that was produced was sufficient to power a generator. And produce more than the input energy.
How can that be? Say the sceptics. Well I don't know, but apparently the system was presented by Cornish to BMW who road tested it and alledgedly said it worked - of course the letter from BMW could be a fake, anyone want to write to BMW and ask them?
Real Cornish design can be seen here
Downsides to this, would be, if everyone did it the cost of aluminium would go sky high as demand outstrips supply. And creating aluminim is a very energy intensive process.
Some 20 years later, and some guy on a website said he was contacted by Cornish by email, you can read the story here.
I also found these postings alledgedly from F P Cornish using his trade mark "big boys" terminology and proffpc username.
scroll down to the highlighted words
A recent Amazon book review - on one of his favourite topics, curing disease
A comment on a current affairs site
A very recent post from him
His activity on Wiki - he considers himself a "French nuclear physicist"
That's about all I can find on him. It appears he does exist and believes in his own creation.