Perfect logic. Sound example young man.

I know. It's much easier than splitting water, burning in, collecting the water product of combustion, and then splitting it again. If you are gonna build a perpetual motion machine, might as well make it simple.
Of course, an even better solution would just be 4 wheels that all drive each other, then you wouldn't need an engine at all. Just 4 wheels and some gears or belts or something.

That's called an alternator

"Facepalm"
An alternator charges the battery in a gasoline-powered vehicle. A battery which is only used to start the car and provide trickle power to stuff like the clock and alarm while the car is off, not as "fuel" for the engine. There's no use for an alternator in an electric car, because it does absolutely nothing but waste energy.

Are you guys trolling me? Am I being trolled right now? Surely everyone has heard of the conservation of energy.

Of course they know of the conservation of energy

But look here - Article on getting a flame from salt water using radio waves.

http://news.nationalgeographic.com/news/2007/09/070913-burning-water.html

This is just standard electrolysis of water. The only difference is that he's using radio waves rather than an electrical current. Here's a bigger article on it with some background on the guy and his discovery:
http://auto.howstuffworks.com/fuel-efficiency/alternative-fuels/salt-water-fuel.htm

Quote from the article:

This is of course 100% correct. Now I can think of scenarios where the water might be useful for propulsion, but they would always keeping russian's statements true:

1. You have an engine (maybe nuclear powered) that ejects a material at high speed out the back of the ship. This material could be water, and when you run out of water you need more. Of course this water is not a fuel or a power source, it is just a material you are throwing out the back. Like a kid on a skateboard who throws baseballs forward to make him travel backwards, the energy source is his arm, not the baseballs; but you do need a good supply of baseballs.

2. You arrive at Europa and set up some equipment to extract energy from the local region: geothermal, wind, hydro electric, or solar; I have no idea which of these---if any---would be viable on Europa. You then use that to preform electrolysis on the water to get hydrogen to fuel your rocket.

But to reinforce what russia said before: there is no way to build a device that repeatedly extracts work from water, without investing more work into the system (taking a net loss).

Well, at least we haven't found a way yet
Fusion could potentially work. We crack water, vent oxygen, fuse hydrogen into helium, use the energy to crack more water. Consume water, produce oxygen and helium as waste products, and get net energy.

yeah i wasn't considering the strong force, on paper with fusion you can get return from anything lighter than iron. But yeah, I don't think anyone is considering bring a portable fusion power plant to Europa.

Ding ding... and this is what he was talking about when he said water is a fuel source. I don't think anyone suggested bringing water back to earth or using magic to split water into hydrogen and oxygen.