Can this also be used as "I can go home early because there is no teacher" or is it clear that the subject is we
Yes and no.
Yes you can use "I" instead of "we".
No, it's not clear because this is a sentence without context. Given more context, you would know which pronoun was correct.
"if the teacher doesn't show up in 15 minutes we are legally allowed to leave"
Wouldn't we say: We can go home early because the teacher didn't show up. ? OR, We can go home early because the teacher isn't there. ?
First one, I would say no because not showing up is like saying the teacher didn't come, which is a different verb (선생님이 오지 않았기 때문에 ...).
Second one is OK but the current Duolingo translation is the most accurate.
Is it okay to remove 우리는?
Yes, the word 우리 is implied in this sentence. More often than not the subject is dropped from sentences because it's obvious who you are referring to.