What is the timing for Sabotaged Armaments versus weapons like Power Punch?

Sabotaged Armaments is revealed when one of your characters defends, before Battle Cards are flipped. Power Punch will be scrapped before it can affect that battle.

If an opponent attacks me with a Sturdy Javelin on a ranged character and I reveal a Sabotaged Armaments I played last turn, how do the cards resolve? Does the Javelin scrap and deal two damage before the secret action takes effect or does the secret action scrap the Javelin before the two damage is dealt?

The attacking player will scrap the Javelin to do 2 Damage. Because attacker effects resolve before defender effects.

When you use Sabotaged Armaments, and your opponent has a Power Punch on the attacker, do they get the Bold before Sabotaged Armaments activates?

No. This all happens before Battle Cards are flipped. Speaking of which, what happens when a character upgraded with Anticipation Engine swings into a Sabotaged Armaments? Anticipation Engine and Sabotaged Armaments will both trigger at the same time. The attacker will resolve Anticipation Engine first, then the defender will resolve Sabotaged Armaments.