Translation:On my way!
I think the main acceptable translations should be I am (He/She/It is) going, rather than the idiomatic expression. One thing i would change about this course is to use only literal translations for the main lessons, and utilize the Idiomatic Expressions feature like the Spanish course does if it wants to teach these kinds of translations. I would also force the students to learn how to use words such as I, He, She, etc. so it's not so confusing to translate.For example, instead of saying 갑니다 means I am going, the korean should explicitly state 제가 갑니다 or 얘가/걔가/쟤가/것이 갑니다.
I know you are correct. 갑니다 It was explained in another course. The "go" in this case is not the lliteral going to somewhere else. it's more like going from where you are. Therefore the idiom is a norm for "on my way!"
My idea is to tbink of it like thus: on my way out from this place and coming to where you are.
No, the verb "가다" means, "to go" and here it utilizes the polite ending "-ㅂ니다." The translation is idiomatic in this example, but in general does not imply a subject of the action. Verbs do not conjugate in Korean like they do in Spanish or French, so "갑니다" could just as well mean "he goes" or "they go" depending on the context in which it's found.
Edit: nice ninja edit.
The translation they used is a loose translation, not a literal one. So literally, it means:
But in a colloquial sense, it means:
I'm going! or I go!
And in a loose translation, it can mean "I'm on my way." (I don't like that they used a very loose translation for this)
Also, look at my comment above and you'll see I talk about I/He/She/It etc. :)
Though you're right to say "Let's go" is an appropriate translation, it wouldn't be right to say it is more accurate.
자 is a suffix that carries the meaning "let's/let us" You use it by taking the verb stem (drop the 다 from the end of the verb) and adding it to the end.
가자 would mean "Let's go"
같이 공부하자 would mean "Let's study together"
우리가 어릴 때 갔던 공원에 찾고 가자 would mean "Let's find and go to the park that we went to when we were young"