"No people are living in this forest."
Translation:Ebben az erdőben nem laknak emberek.
I think the above translation is good enough. But maybe "Senki sem/nem lakik ebben az erdőben." is more literal, and also good.
Your suggestion: "Nincsenek emberek, akik... " is not how a Hungarian would phrase this. But a close alternative is "Nincs olyan ember, aki ebben az erdőben lakik." But, still, this sentence focuses on the people, not the forest. The other versions emphasize the forest being without human inhabitants.
Also there is ameaningful difference between "people don't live in this forest" and people are not living in this forest" (this can also be stated as "no people are living in this forest"). The use of "don't" implies a habitual refusal of people to live there. The use of "are not" implies people might live there sometimes, but not at present.
If laknak wasn't there, then it would be correct?
Ebben az erdőben nincsenek emberek
are no people in this forest.
Once the additional verb comes in, it makes the nincsenek incorrect.
Ebben as erdőben nem emberek laknak
This needs to be in the tips, too.