No, that's not written correctly. Aluminum metal doesn't react with hydrochloric acid (a solution of hydrogen chloride gas in water) to generate AlCl3 and water, because AlCl3 is unstable in water, and reacts further. Besides, you can't just pick random reactions to try to balance. You have to have some knowledge of some of the products. Generally experimentally, although there are some hints from solubility rules, electronegative, and more complicated methods.
And no, I doubt there is an inert liquid solvent for most metals. Well, maybe mercury, or gallium. Bu the result is more alloy than solution.