Can we just take a moment here to appreciate the simplicity of german.... the thing to fly, thing to make fire, thing to drive, thing to play... love it!
I used to live with germans a few months ago, and they taught us to say "Hast du Feuer?" when we needed a lighter. Is this normal to shorten it just to fire instead of the compound word, and if so are there other words that it's common for?
I think in English you'd say "Do you have a light?" accordingly. "Hast du Feuer?" isn't an abbreviation of "Feuerzeug", but refers to the actual fire coming out of a lighter or from a match.
I think there are words that get shortened in German, like "Auto" for "Automobil" (but nobody says "Automobil" anymore anyway, so it doesn't really count), or "Defi" for "Defibrillator" (but I assume that's just an abbreviation medical staff use to speed up the conversation), but I can't think of any [proper ones] at the moment. Maybe you'd like to ask this question in a new thread, there might be some interesting answers.
In spanish we say literally the same, at least in Mexico where I live. "¿Tienes fuego?" "Hast du Feuer?".
To me, a "fire-lighter" is a small block of solid fuel to help with starting a fire. Not the same thing.