I understand that gamma-rays can produce positron-electron pairs and positrons and electrons can annihilate to two gamma-rays.

My question is: If a gamma-ray photon creates a positron-electron pair, will the two particles "instantly" annihilate again because of their positive-negative-attraction and create two photons (each photon with half the energy of the original gamma-ray photon)? Or do they travel apart from each other (and then do stuff on their own)?

For the first case: Is this occuring until such low energy photons are created which then can't produce matter-antimatter pairs anymore?