The very first post in this thread explains the rules of the challenge. Choose one type (Steel in my case, but there are also Normal and Electric games going on currently) and your battlers must all be of that type. Move type is irrelevant, so no, just because you teach a Quagsire Iron Tail does not mean it qualifies. (Shame, it'd come in handy against Fire-types, easily my biggest weakness now that Steelix isn't Rock-type anymore.) And no, there aren't any other Steel-type moves than those four.