Translation:There are no people living in this forest.
It really does seem that "nem" modifies "laknak" and not "emberek" because of proximity and word order. So I expected "do not live" instead of "no people."
You are right. This would be a more accurate translation.
And yes, nem always modifies the word (or phrase) coming right after.
I would translate the given English sentence with "Ebben az erdőben sehány ember nem lakik." (more literally "No number of people live in this forest.")
Perfect but the person who wrote the translation at DUO is forcing us to copy and paste an incorrect answer AND there is no choice to say that the ENGLISH translation is wrong or awkward, only that the Hungarian sentence may have errors or be awkward.
Only if there were no other verb. Note that "There are no people living" is a continuous tense, which doesn't exist in Hungarian.
This sentence is not an example of the illative case (-ba, -be) which indicates movement towards a space, and which is the object of this exercise. Ebben in an example of the Inessive case (-ban, -ben), which indicates position in a space.