Eldar codex (4th edition era, copyright 2006), Eldar 6th FAQ v1, and 6th edition main rulebook.
The main rulebook states that Witchfire powers are used as Assault weapons in the shooting phase (but uses no language stating they may only ever be used in the shooting phase). The main rulebook states that Witchfire Powers are also known as Psychic Shooting Attacks. The main rulebook states that psykers regain Warp Charge at the start of every turn, and that unless specified, every turn means the player turn, not the game turn. The Eldar FAQ for 6th edition, v1, declares that Warlocks are Mastery Level 0 (zero), and thus do not have Warp Charge (rendering any Warp Charge argument moot). Likewise, the codex states that their powers are always on and do not require a Psychic Test (rendering any Psychic Test argument moot). Further, the FAQ enumerates which Eldar psychic powers (including Warlock powers) are psychic shooting attacks (a carryover from the 5th edition Eldar FAQ). One of these listed is Destructor. Thus, Destructor may be considered a Witchfire power. The Overwatch rules allow the use of a Snapfire shooting attack, though Snapfire bans Blast and Template Weapons, but the Wall of Death rule allows the use of Template weapons, but only in Overwatch. Destructor uses a Template.
Answer 1: Destructor may be used in Overwatch.
Answer 2: Destructor may not be used in Overwatch, because there is nothing specifically stating that Witchfire may be used at any time other than the shooting phase (despite the lack of language allowing other weapons to shoot out-of-phase, spare the Overwatch rule). This applies a stricter standard of scrutiny to Destructor than to other shooting attacks because it is a psychic shooting attack.