Kha'Zix, Mutating Horror

No. Even if an opponent can legally play a unit in reaction, that unit's arrival does not undo Kha'Zix's fulfilled trigger condition.

Kha'Zix's ability reads "When I attack or defend, if an enemy unit is alone here, give me +2 this turn and gain 2 XP." The "if" clause immediately follows the initial trigger clause, so it is part of the trigger condition.^383.2.a.1 The condition is evaluated once, when Kha'Zix gains the attacker or defender designation.^{383.4.e.2.a383.4.e.2.b383.4.f.2.a383.4.f.2.b} If the enemy unit is alone then, the ability is placed on the chain.^383.3 Because the "if" clause is part of the condition rather than the effect, the effect does not check it again during resolution.^383.2.b407.5 If the enemy unit is not alone then, the ability does not trigger even if another enemy unit is later removed.

Playing a legally timed unit places it on the existing chain as a pending item.^330.2420.1 After it finalizes, the unit resolves immediately and enters the board.^337.2359.2.c This later entry does not repeat Kha'Zix's earlier trigger-condition check.

Yes. In each combat, Kha'Zix can trigger when he first attacks and when he first defends, if an enemy unit is alone at his battlefield at each check. Attack and defend trigger conditions are checked separately when a unit first gains the matching designation during a combat.^{383.4.e383.4.f} Each matching check happens only once per combat, rather than once per turn.^{383.4.e.2.a383.4.f.2.a}