Translation:People do not live in this forest.
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.")
Boveka, there's no problem with saying "Someone is living somewhere." The progressive form is often used if you're talking about a temporary living situation.
Quote from the book "Aspect" by Bernard Comrie, p. 37:
Thus if I say I live at 6 Railway Cuttings, I imply that this is my normal residence, whereas if I say I'm living at 6 Railway Cuttings, I imply that this is only a temporary residence (for instance, while my Mayfair flat is being redecorated).