If a ship with advanced cloaking device fires at a ship of the same pilot skill, but has initiative, does he perform his cloak action before or after the defending ship returns fire?

Clarification much appreciated. Trying to avoid an argument this Sunday.

Yes, the Phantom will finish its attack and trigger any "after attack" effects like ACD. The Phantom will be cloaked when the other ship shoots back at the same PS level.

As Dr Lucky said. If you attack first you get to finish all of the things that attacking allows first.

The trick to this one is that "simultaneous attacks" really aren't simultaneous at all; it's a flavor name rather than a mechanics one. The Simultaneous Attack Rule does exactly one thing. It delays a destroyed ship's removal from the board. All other abilities and game effects proceed as usual.

Does this mean a destroyed ship with no initiative but same PS can shoot and use Vader prior to blowing up?

Ships don't have initiative, the player does. It is only used to decide timing issues, and in the case of the Simultaneous Attack rule (two ships with the same PS), the player with initiative attacks first, and then the player without initiative makes his attack, including Vader.

Keep in mind that the Simultaneous Attack rule only applies if one of the ships is destroyed before getting it's chance to attack. It merely keeps it in play until it has made it's attack. Once it's attack is done, it's removed as normal.

Does this mean a destroyed ship with no initiative but same PS can shoot and use Vader prior to blowing up?

Once upon a time yes, but vader has and FAQ entry now saying you need at least 1 hull to trigger him. Sad face