If you're only going to allow "let's" then the verb should be 가자 or 갑시다.
Isn't "Let's" 갑시다?
That is the formal "let's" and this is the less formal but still polite "let's"
But how do we know that it's a ''let's go'' and not an ''I go''?
You don't. It depends heavily on the context.
Then the course should accept "I go" as another possible answer.
They won't if they mean you to only practice THIS specific meaning at this moment. It's more of making sure you understand both at any time, so they insist on special meanings on special lessons.
I agree with @FBahar1
My guess is DLG wants to show us, learners the ambiguity of 해요체 in writing, before introducing us to the use/importance of auxiliary verbs sa ~나요; ~지요; ~세요; ~는 게 어때요; etc.
Rather than less formal I would say that they are both formal but "갑시다" is more respectful while "가요" is a friendlier and casual way of saying "갑시다".
Should be 갑시다 or 가자.
From my understanding 가 is to "go" and using ㅂ시다 or 요 is depending on how formal you are speaking. The word "Let's" is omitted, it is implied when the speaker puts it into action, like "하지 or 하다" in this instance 가요 let's go.
Right. The original form of the verb is 가다, and the usage varies on which 'verb endings' you use in a sentence. I personally like to compare it with conjugations in several European languages.
Why can't this be "I go home in the afternoon" or " Go home in the afternoon" ?
I go home in the afternoon, (Yes).
Go home in the afternoon - imperative form. (No)
This would translate as:
오후에 집에 가세요!
"Go home in the afternoon" isn't accepted