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Slight. As with Are να and ας translated identically when used with a first person plural verb in Modern Greek?, it’s mostly a nuance thing: ας φύγουμε: “let’s leave, how about we leave”: pretty weak sauce, gentle prodding πρέπει να φύγουμε: “we must leave”, strong implication that this is an external imposition να φύγουμε: “we […]

Not quite. In the existential sense that you’re using, είναι ένας άνθρωπος means “it is a man”, and υπάρχει ένας άνθρωπος means “there exists a man”. The latter sounds as formal and logical in Greek as it does in English, though I think it is more widely used than English as an interrogative or negative. […]