If I have Focus Sash attached to Marshadow & Machamp GX and then use its "Acme of Heroism GX" attack, which one takes precedence if Marshadow & Machamp GX would be KO'd by damage from an opponent's attack?
You would choose, as they have the same effect, you choose the order of resolution.
Source: TPCi Rules Team (2019-06-27)
If Lysandre Labs is in play and I use Primal Groudon's "Gaia Volcano" attack to discard the stadium and do enough damage for KO, what happens if the full HP Fighting-type Defending Pokemon has Focus Sash attached to it?
While Lysandre Labs is in play Focus Sash has no effect. However, Lysandre Labs is discarded as part of the attack before KO's are checked. So the Focus Sash would be in effect and if all of its conditions are met the Defending Pokemon is not KO'd but has 10HP remaining.
Source: TPCi Rules Team (2018-05-31)
What happens if Shining Jirachi with Choice Band attached uses its "Stellar Reign" attack against an undamaged, evolved, Lucario GX with Focus Sash attached? Does Focus Sash save the Pokemon from a KO?
During the attack Stellar Reign would do 80 damage (10 for the attack plus 30 for the Choice Band, then times 2 for Weakness). Then the devolution part of Stellar Reign would return all Evolution cards to the opponent's hand. However, when KO's are checked the devolved Pokemon is not the same Pokemon that was attacked, so Focus Sash would not protect the newly devolved Pokemon. The original Pokemon took damage from the attack, and the lower Stage just happens to have enough damage on it for a KO.
Source: TPCi Rules Team (2018-05-31)
If the Pokemon that Focus Sash is attached to is attacked with an attack such as Cobalion EX's "Steel Bullet" that ignores effects on the Defending Pokemon, is it Knocked Out?
No. The full damage would be done first, and then afterwards the effect of Focus Sash would reduce the damage counters to leave 10 HP remaining.
Source: Furious Fists FAQ (2014-08-28), TPCi Rules Team (2014-08-28)