These are the deployment instructions for the Pup:

From reading that and applying existing rules, I think the following is all true:
1. If the Pup deploys with a K-Turn it does not receive a stress as there is no Check for Stress step in the deployment instructions. <it looks like the K-Turn puts you in the same spot and facing as the 3 straight would>
2. Even though it is the same pilot that was in the Yv-666, the Pup is able to take any action on its bar regardless of what action the YV-666 took earlier in the round since it is a different ship.
3. In the case of simultaneous fire, the Pup is not deployed until after the YV-666 has had a chance to attack.
Edited by WWHSD