Substantially correct. A man must marry before ordination to the diaconate, not necessarily before entering seminary. A cleric cannot remarry, even if his wife should die. And Eastern bishops are chosen from among monks, who are always celibate. An ordinary diocesan priest isn’t eligible, unless he was ordained as a celibate, or widowed, etc.
Was this thread posted because of talks about allowing mature men in Brazil who are married to become priests?