Κουμπάρος here means either best man or someone who is the godfather of one's child. It does not matter which because both are equally important relationships.
Τελειωσε= it's over. I don't know how Cypriots talk, and I think you should stick to standard Greek which is spoken and understood by all Cypriots and also written by everyone in Lexi. This is to avoid confusion, as there clearly is some confusion here. Ετελείωσε especially when said like in the film clip means exactly what it means in the clip (and the word has become a sort of catchphrase because of this film and its 1960s remake). So what you are getting here is a snippet of popular culture, not a grammar lesson. Ετελείωσε= it's sorted (but not really).