I have a Scuttle Crab on a battlefield and my opponent has Nidalee. He wins a combat so he gets to draw one. My Deathknell says I can look at opponent's cards. Do I see the card he draws?

No, you do not see the card Nidalee draws.

According to the RiftJudge FAQ #10347 and the specific timing rules governing the Combat Cleanup phase, Scuttle Crab's Deathknell ability resolves completely before the combat win is even acknowledged, which triggers Nidalee’s draw ability.

The Sequence of Events (Rule 461.1, 461.2):

1. Combat Cleanup: Scuttle Crab takes lethal damage. Its Deathknell triggers as a "Pending Item."
2. First FEPR Window: Scuttle Crab's Deathknell is placed on the chain and resolves. Your opponent reveals their hand at this moment.
3. Determine Combat Result: The game determines the winner of the combat. Since Scuttle Crab was defeated and Nidalee remained, Nidalee is declared the winner. This triggers her "When I win a combat, draw 1" ability as a new "Pending Item."
4. Second FEPR Window: Nidalee’s draw ability is placed on the chain and resolves. You draw your card after the Deathknell reveal has already concluded.

Because these abilities occur in separate processing windows (FEPR - Finalize, Execute, Pass, Resolve), the draw from Nidalee happens after your opportunity to look at the opponent's hand has already finished.