Can you activate Stardust Phantom's effect during your opponent's turn in Yu-Gi-Oh?

Answer 1

Stardust Phantom's first effect is a Trigger, and will activate whenever the condition is met. That means it can activate in your turn or your opponent's turn.

Stardust Phantom's second effect is an Ignition Effect and can only be activated in your own turns. The protective effect it applies to a Synchro Monster will work like a continuous effect, it can be protected once per turn in either player's turn.