Does Giant Killer get destroyed with Warstorm Surge? or is it able to destroy my creature with it's instant ability?
You seem to be misunderstanding how Adventure cards work.

Once Giant Killer is on the battlefield; the Chop Down instant/adventure does not do anything. Adventure allows you to cast the Adventure part from your hand like a normal instant/sorcery. When that spell resolves, it is exiled, and while it is exiled, you can cast the creature from exile.


  715.3. As a player casts an adventurer card, the player chooses whether they cast the card normally or as an Adventure.
  
  
    715.3d Instead of putting a spell that was cast as an Adventure into its owner’s graveyard as it resolves, its controller exiles it. For as long as that card remains exiled, that player may cast it. It can’t be cast as an Adventure this way, although other effects that allow a player to cast it may allow a player to cast it as an Adventure.
  


So your friend cannot do anything with Giant Killer's adventure; your Warstorm Surge triggers when you play Gisela, and if you choose to target Giant Killer, it will take 10 damage (5 which is doubled by Gisela) when the triggered ability resolves.