when scuttle deathknell activates, does the player get to see the hand as much as he want

No — the hand reveal is a one-time, temporary action, not standing permission. You reveal for only as long as it takes everyone at the table to clearly read and understand the cards, then the hand goes back to private information (Rule 424.3, 424.1.a.3).

The two halves of Scuttle Crab's Deathknell work differently: "they reveal their hand" happens once and ends immediately after it's understood, while "you can look at their facedown cards this turn" is a standing permission that lasts the rest of the turn — so new Hidden cards they play later that turn are still fair game to look at.

You can't re-check the hand later in the turn, even if they draw or play cards after the reveal.