Yes, but it requires very dangerous amounts of electrical current to produce hydrogen as quickly as this. It also requires a more complicated setup to get hydrogen only, rather than a dangerously explosive mix of hydrogen and oxygen.

You are incorrect. There is no oxygen involved with this reaction whatsoever.

2Al(s) + 6HCl(aq) --> 2AlCl3(aq) + 3H2(g)

The water dilutes the acid so that the reaction is slowed to a controllable pace. It also helps to reduce bubble formation.

That's called a balanced chemical equation. It just tells you how many of one atom or molecule must react with how many of another to result in a whole number of products. If all you started with in the equation was:

Al + HCl --> ?

The products would have to be listed as fractional values, since there are not enough atoms given to allow you to form the complete molecules. Instead, the reactants are multiplied individually until they make a whole number of products, with no unreacted chemicals left over:

2Al + 6HCl --> 2AlCl3 + 3H2

This gives you a molar ratio that can be used to determine exactly how much aluminum or hydrochloric acid to react with a given amount of the other to have none wasted in the end. The equation tells you nothing about the quantity or concentration of chemicals that might be used to preform this reaction, it only gives a ratio, and shows all the chemicals involved.

If you wanted to do the math you could determine exactly how much HCl was in the 300 mL, and then from the equation calculate exactly how much aluminum would be needed to use it all, but I find it much easier to simply add the aluminum until it no longer reacts. Even if you did do the calculations, you could not add all the aluminum at once or it would react far too violently to be controlled, resulting in boiling acid spraying everywhere.

The hydrogen is not removed from water in this reaction, it is removed from hydrochloric acid, HCl. The chemical equation in my previous comment explains what happens to all elements involved.

I can't really tell you much without witnessing what you're doing. Would it be possible for you to record a video?

Is your acid the same concentration as what I show in the video?

Not very safe to be firing a toy rocket near a flask of acid.

If it used crystals it sounds similar to a carbide cannon, in which case the fuel was acetylene, not hydrogen. Calcium carbide produces acetylene when dropped into water, which is what a number of replica cannons use for a loud report. Never heard of its use in a rocket, but it might be worth asking the manufacturer or checking online if that was indeed the fuel, in which case you may be able to find it under a different brand.

NaOH is also commonly available in hardware stores and supermarkets, marked as Lye.

Red Devil or Rooto