"I am from Korea."
Translation:저는 한국 출신입니다.
네가 would be used with people you are considered close with. Its an informal way of referring to oneself so think of it like talking with close friends or family sort of language. You wouldn't talk informally around people you don't know well or people of a higher standing or greater age than yourself as it would be considered rude.
The module is specifically about certain verbs, so they want you to practice what they give you, not other words. And if you look at the notes of the very next module, it says that it's starting us out learning a speech level which is used when talking to strangers, so it's more on the formal side than the informal.
First, 저 is the formal way of writing "I" and 나 is the informal. So, 저는 is formal and 나는 is informal.
Then, there's 제가 and 내가. Grammatically, both mean "mine", but people often use both for "I" and "me".
제가 is a contraction of 저의가. 내가 is a contraction of 나의가
You'll also see 네가 (contraction of 너의가) for "you" in books, but people don't say it that way because it sounds the same as 내가.
1) "저는 한국에서 왔습니다." 오다 means come. 왔다 (왔습니다) means came. So, this sentence literally means "I came from Korea." and it only makes sense to say this sentence if you are not in Korea.
2) "저는 한국 출신입니다." 출신 means native/origin. The sentence means that your a native of Korea, although if you changed 한국 to a university name, it would be stating what your alma mater is. Also, the sentence makes sense regardless of where you're located.
No article is needed.
Korean student = 한국 학생 Korean food = 한국 음식 Korean movie = 한국 영화
출신 = native but it can also mean origin, birth, affiliation, as well as a graduate (of a particular school)
So, 한국 출신 means "Korean native".
"저는 한국 출신입니다." means "I'm a Korean native." or "I'm a native of Korea."
But in a way, it's not the same as "I'm from Korea."
"Korean food" is 한국 음식 (Korea + food).
"Korean music" is 한국 음악 (Korea + music).
출신 means native. "저는 한국 출신" means "I'm a Korean native." or "I'm a native of Korea."
If you want to say where you're from using the location marker, you could say "(place)에서 왔습니다." It literally means "I came from (place).", so it only makes sense if you say it when you're located someplace else.