I am having trouble understanding how to create equations which can then be balanced. For example, if I am told that a freshly scraped piece of aluminum reacts with oxygen from the air to form a protective coating - where does the unbalanced equation $\ce{Al_{(s)} + O_{2(g)}-> Al_2O_{3(s)}}$ come from? In that, where does the $\ce{O_3}$ come from in the product? Following a synthesis $\ce{A + B -> AB}$, how am I to know I get 3 oxygens within the product of aluminum oxide, and why can't I say $\ce{Al + O_2 -> AlO_2}$?
Then take the reaction of fresh scraped aluminum with hot water, where the products of reaction are aluminum hydroxide and hydrogen gas: $\ce{Al + H2O -> Al(OH)_3 + H_2}$. How do I actually determine that these are the products in the first place, and how do we get the $\ce{(OH)_3}$ in the reaction equation? Following a single replacement $\ce{A + BC -> AC + B}$, what is wrong with saying $\ce{Al + H2O -> AlO + H_2}$, and then balancing?
Sorry if this is preschooler stuff around here, but will appreciate any guidance.