This is a bit of a tricky subject.
I believe the first is more grammatically correct, however the third is likely more common in speech.
"Youth" is a singular noun, therefore it takes the pronoun "it" and conjugation "has."
For example, "Youth" should be treated the same as "apple":
"The apple has not rotted yet. However, it does smell bad"
The fact that "youth" in this case refers to a collection as opposed to a single person plays no part.
However, in common practice, you would likely see the last case. The reason for this is that on a case by case basis, when using a pronoun, we cease to refer to "youth" as a unit, and instead refer to them as individuals. For example:
"Today's youth smells bad" --> Here we could replace "Today's youth" with "it".
However,
"Today's youth should shower more often" --> Here we could replace "Today's youth" with "they".
I would absolutely never say "Today's youth should showers more often", even though "should showers" is the singular conjugation.
Even to my ears, the third sounds the most natural.