The 打 in 打火機 is more like hit in this context. Makes a bit more sense with the way older lighters required you to flick it. But 打 is also used in a ton of contexts haha.
The second character, 鵝, means goose. So 企鵝 is literally something like, "standing on tiptoes goose". But no one would look at it that closely, to everyone it's just a penguin.