Gel Rocket

Gel ethanol (a mixture of ethanol and acetate / calcium ethanoate) can burn, it's true. But is it enough to become a solid propellant rocket for a rocket enthusiast? I mean, the rocket just need hot gas, not an explosion. In addition, the nozzle will be responsible for most of the rights to produce thrust?

A booster rocket with solid fuel, by definition, contains the oxygen needed for combustion of the fuel element. Gunpowder, for example, and nitrates, containing atoms of oxygen for the oxidation process to take place explosively.
The freezing of ethanol can not and does not burn without oxygen source, if in spite of its gel state, is really a liquid fuel in gel form, and would require an additional source of oxygen to be mixed with her in the combustion chamber.
You are right not to require an "explosion" but you need a bonfire, quick, very large volume of gas produced, and this requires a source of oxygen.