Does my Deathknell of Scuttle Crab resolve after conquering or before?

To answer your question, your Scuttle Crab's Deathknell effect will resolve before you establish control of the battlefield and potentially conquer it.

The Reasoning

The timing for these events is determined by the specific steps of a Combat or non-combat Showdown's resolution:

1. Deathknell Triggering: When a unit with Deathknell dies (for example, due to lethal damage in combat), its trigger is added to the chain as a Pending Item during the cleanup process (Rule 808.1.d.2).
2. Resolution: The game returns to the standard process to resolve the chain (the FEPR process). Your Scuttle Crab's Deathknell effect resolves during this step (Rule 808.1.d.3).
3. Conquering: According to the combat/showdown resolution flow, establishing control and conquering a battlefield happens after the resolution of chain items and combat cleanup tasks have been completed (see Rules 348.2.a and 461.5.d).

Summary of the Sequence:

1. Combat/Showdown Cleanup: Units take damage; if Scuttle Crab is dealt lethal damage, its Deathknell triggers and is added to the chain.
2. Resolution of Chain: The game processes the chain items. Your Scuttle Crab's Deathknell resolves, and your opponent reveals their hand.
3. Establish Control/Conquer: Once the chain is empty and the combat/showdown cleanup is finished, the remaining player at the battlefield establishes control and performs the Conquer action (if they haven't already scored that battlefield this turn).

Therefore, the Deathknell effect occurs before the battlefield conquer is finalized.