Can I play Target Whistle and choose a Basic Pokemon in the Discard Pile with the Omega Barrier Ancient Trait, or does Omega Barrier block the Target Whistle?
Yes, you can put that Pokemon from the Discard Pile onto the Bench. Ancient Traits are only active when that Pokemon is in play.
Source: TPCi Rules Team (2017-03-30)
Can you use Target Whistle on an opponent's discarded Robo Substitute?
Target Whistle says that it can bring back a Basic Pokemon card, but the Robo Substitute in the discard pile is a Trainer card, not a Basic Pokemon.
Source: Phantom Forces FAQ (2014-11-13), TPCi Rules Team (2014-11-13)