Will it be correct if I say "youth's problems" instead of "youth problems" and "cities' problems" instead of "city problems" when interested in the belonging problems to youth or cities, not only in descriptive function of the attributive units?
Yes, but you have to be careful with such terseness. It is easy to become incomprehensible. You can't rely on syntactic tricks to convey meaning reliably.
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Yes, but you have to be careful with such terseness. It is easy to become incomprehensible. You can't rely on syntactic tricks to convey meaning reliably. "Youth's problems" are acne, insecurity, naivete, etc. "Youth problems" is nigh on inscrutable, but one might guess gangs, loitering, vandalism, etc.