Very interesting. It looks like it is used at a much lower frequency than shoot, and mostly after 1950. Apparently, as with other cases of language development, a misconception has grown so widespread that it has eventually been accepted.
Well, that's true. It is odd that this is the "main" way they have it translated. But with how much work this course needs, this is probably of the least concern. Perhaps they'll be able to clean it up later once the more serious kinks have gotten worked out :)
Root stem is 쏘다. Conjugating words that end with 오 are followed by 아. So 쏘다 conjugates to 쏘아. You can then contract this into 쏴. (think of 보다. Instead of 보아 we write 봐). Past tense is 쏘았어요 which we contract to 쐈어요.