Okay, Urkel, enlighten me. How is aluminum foil 'low grade?' Modern aluminum foil is just that: Pure aluminum, in foil form. It isn't anything else because it would cost more to make it more complicated than that.
Your particle size may affect how well it burns, but with thermite this isn't very critical. As you say, ball milling can also generate finer powder, after you blend the stuff.
Dissolving aluminum in hydrochloric
acid will generate ferric chloride; Adding sodium hydroxide (a base) to the solution will not cause your ferric chloride to convert back to iron or iron oxide. Rather, it will neutralize the remaining
acid and make a big mess. After the strong
acid is neutralized, the weaker ferric chloride will be neutralized, resulting in ferric hydroxide. Useless to us.
You can reduce iron out of ferric chloride by heating in the presence of sodium chloride. This is done in industry by aerosolizing the stuff over a catalyst with equipment you do not have.
A faster way to make iron oxide is to simply burn the steel wool or douse it in acetic
acid (it's vinegar, kids) and then expose to oxygen.