Is water a possible fuel for jet engines?
It can't work because of the fundamental thermodynamics

What you are proposing is, basically, the plane carries water; the water is broken down into its components, hydrogen and oxygen; the components are recombined by burning them as fuel. Burning hydrogen and oxygen is a perfectly good way to create a lot of heat. But it doesn't much matter how you break the water apart into hydrogen and oxygen, the thermodynamics of the reaction won't work.

The problem is simple: you need to have a source of energy to split the water apart. In chemistry we know the energy levels of the reactants and the products and we can work out whether energy is released or stored in a reaction. Burning hydrogen and oxygen releases a lot of energy, but by the rule of thermodynamics, breaking water apart to its components requires the input of exactly the same amount of energy. You can't get round this. Worse, in the real world, there are losses at every conversion step so you can't even break even (ain't things unfair!) 

In your plane you could, in principle, split water and burn it in the engine for propulsion. But you would need to have some other source of the vast amount of energy required to split the water. That implies both another fuel and another engine. In reality they would vastly outweigh any imagined savings in weight and cost.

Even if you could build some sort of SciFi engine that both splits water and then burns it again you would still be nowhere: the entire output of the burning would be required for the splitting with nothing left over to generate thrust (and in the real world there are losses so your plane would rapidly drop out of the sky).