I was given the options "Aloha ʼoe," "Aloha kākou," and "E kāua." The correct answer was given as "Aloha kākou," but I think that means "Hello, everybody," not just "Hello." I also see that "Aloha kāua" is the given translation, but that wasn't even an option for me. In any case, I don't understand why that is the translation either instead of just "Aloha."
I get the feeling that the accepted variations are intentional and not viewed by the creators as incorrect. If there is any error, it is an error in judgement.
They are trying to teach that "Aloha!", "Aloha kākou!", and "Aloha Kāua!" are all basically used as "Hello!"
It is incorrect to say "Aloha ‘oe!" since aloha should always include yourself. "E Kāua" is also incorrect because it doesn't include aloha at all. So, while we might more literally translate "Aloha kākou" as "Hello, everyone" it is the only one of those options which is an acceptable way to say, "Hello".
And the reason the "correct answer" and the "given translation" might differ is that they have been marked as equivalent for this exercise (but not necessarily in other exercises where they might be trying to teach a different point) and the system randomly grabs one for the exercise and then randomly grabs one for the translation and sometimes winds up with different ones.
You were right about our intentions for showing that "Aloha!", "Aloha kākou!" and "Aloha kāua!" can all mean "Hello!" And there were some gaps previously in our accepted answers (Alternate Translations). Those should, hopefully, all be taken care of now, at least for these exercises.
Just a note: "Aloha ʻoe" can also be used to say "Hello" and "Goodbye", but it is not taught here. You may see it in letters or in song, like in the well-known mele composed by Queen Liliʻuokalani.