"He asuvat" should be correct too, right?
Yes, because there's no context for telling if we're talking about humans or other animals.
And He elävät too.
Why ´ne´and not ´he´ ? How do we know which one is applicable?
Both should be accepted. "He" usually refers to humans and "ne" (plural of "se") to everything else, including animals (and in spoken langauge it's used about everything, also humans). Report that if both are not accepted.
Agree that both he and ne should be acceptable
"he" was NOT accepted for me 20-sept-2021. Duolingo considered it a typo and recommended "ne" instead. So this is not completely fixed.
"He" accepted for me late January 2021
"He asuvat", that is