Julius Caesar was the first Roman to have his face put on a coin.
Cleopatra was actually the seventh queen of that name.
Under Roman law, Caesar and Cleopatra could not marry. Ancient Roman law stipulated that marriage was only possible between two Roman citizens. Cleopatra was ethnically Greek and her family had ruled Egypt since the time of Alexander the Great.
Since Cleopatra was not a citizen of Rome (although Egypt was a Roman province), technically Caesar was not committing adultery. As if Caesar would have cared-he seduced many of the wives of his political opponents in Rome.
By Roman custom, by Caesar publicly raising the baby over his head he was declaring himself it's father.