I would have used: "Молоді знають цей театр." ("The young people/ the youth know this theatre.")
Youth is a group, meaning one group, so the verb is singular third person.
Strictly speaking, yes, that argument can be made, but that usage is not idiomatic, at least not in North American English. If the subject were "people", which would also be used as a collective noun in this example, the correct verb form would definitely be third person plural, rather than singular.
"The youth", meaning young people collectively, taking the third person singular is not common in the UK either, certainly not in a sentence like this with no context. "The young people know this theatre", or indeed "Youths know this theatre", would be fine, as would something like "You won't find many older people here, but the youth know this theatre".
When encountering "the youth" on its own, my first reaction is that it's one singular youth ... so I think if the intention is to indicate young people collectively it needs clarifying.
Yes it's singular, but we use notional concordance. IE a singular noun with a plural verb form. We do this a lot with collective nouns.
"The youth knows" refers to an individual and not a group.
It could be either singular or plural and be acceptable. I think the article "the" sounds better with "youth"