In Elder Sign how does removing a monster via a card effect work?
Coincidentally ti me asking, Elder Sign Omens just came out, and i was able to find out how some of these rules function in the digital version of the game.

As a disclaimer Omen rules are not identical in some ways to the paper board game. This particularly applies to when spell cards are used.


  Can either item/spell be used mid-adventure?


Yes they can be used at any roll


  When the monster is removed, does it reveal the task underneath that
  now must be completed?


The task below a defeated monster does not have to be completed


  When using the flute, does defeating the monster count as a success
  and allow a re-roll without assigning any dice nor losing a die
  (normal success)?


No the monster is removed outside of die rolling.  You must still place dice on one of the tasks, or resolve a failure.