Opponent has one unit on the battlefield. I attack with one unit. Then he casts in reaction Shen Kinkou. Can I cast my Kha'Zix Mutating Horror in response to his Shen, and does Kha'Zix get the +2 Might?

Yes, you can cast Kha'Zix in response to Shen. But Kha'Zix does NOT get the +2 Might.

Here's why: Shen was played first (added to the chain by your opponent as a Reaction), then you responded with Kha'Zix. During the Finalize step (Rule 337.1.b), pending items are finalized in the order they were appended to the chain. So Shen is finalized first and enters the battlefield before Kha'Zix does.

When Kha'Zix is then finalized and enters, the opponent already has two units at the battlefield (their original unit + Shen). Kha'Zix's ability checks "if an enemy unit is alone here" at the moment he gains the Attacker designation (Rule 383.4.e.2.b, 459.2.b.3.a) — with two enemy units present, the condition is false and the ability never triggers.

This is different from the FAQ scenarios where Kha'Zix enters first and then the opponent responds with a unit. In those cases the trigger was already placed on the Chain before the second unit arrived and isn't revoked. Here the order of entry works against you — Shen gets there first.