I would like it if the FAQ for Neutron Shark on page 29 of the rulebook was updated to specifically specify whether the top card of the deck still gets discarded or not. The way that it is worded I believe the answer is yes, but being absolutely certain would make me feel better.

This ruling would help me understand if a destroyed card's ability ends immediately, or if it ends after it finishes resolving (and it just can't be repeated if it is destroyed). This FAQ is the only section of the rulebook I can find that touches on the idea that an ability would end if the card is destroyed. Every other section dealing with destruction and abilities is about how destruction prevents the ability from triggering in the first place.

The discarding of the top card is still part of the effect, so yes.

This is an inference from some clarification provided in Crucible Cast #4, where it is stated that if Neutron Shark's effect happens and the controller of Neutron Shark has an empty deck, the effect cannot repeat.