Did Caesar bring Cleopatra to Rome?

No, Caesar summoned her to Rome. There's a difference. Caesar had established Cleopatra and her brother on the Egyptian throne, but the senate had to confirm their status as Allies. An allied kingdom had privileges and also responsibilities. The senate had to debate this and hear from the Egyptian representatives. It was much more efficient to have Cleopatra, on the spot to give answers, than to have her in Egypt writing long distance letters. By the way, Cleopatra never entered Rome itself. She was confined to Caesar's villa across the Tiber outside of the sacred city walls, the pomerium. This was because the Romans had a long standing rule that no crowned head could enter the city.
No, Caesar summoned her to Rome. There's a difference. Caesar had established Cleopatra and her brother on the Egyptian throne, but the senate had to confirm their status as Allies. An allied kingdom had privileges and also responsibilities. The senate had to debate this and hear from the Egyptian representatives. It was much more efficient to have Cleopatra, on the spot to give answers, than to have her in Egypt writing long distance letters. By the way, Cleopatra never entered Rome itself. She was confined to Caesar's villa across the Tiber outside of the sacred city walls, the pomerium. This was because the Romans had a long standing rule that no crowned head could enter the city.