Kozilek's Return

609.7a If an effect requires a player to choose a source of damage, he or she may choose a permanent; a spell on the stack (including a permanent spell); any object referred to by an object on the stack, by a replacement or prevention effect that’s waiting to apply, or by a delayed triggered ability that’s waiting to trigger (even if that object is no longer in the zone it used to be in); or, for certain casual variant games, a face-up card in the command zone. A source doesn’t need to be capable of dealing damage to be a legal choice. The source is chosen when the effect is created. If the player chooses a permanent, the effect will apply to the next damage dealt by that permanent, regardless of whether it’s combat damage or damage dealt as the result of a spell or ability. If the player chooses a permanent spell, the effect will apply to any damage dealt by that spell and any damage dealt by the permanent that spell becomes when it resolves.

For the triggered ability on Kozilek's Return, which object is the source of the damage?
The card in the yard or the card in exile?

If it's the card in exile dealing the damage and I use a spell or ability in response to the trigger that allows me to prevent damage of a chosen source, can I choose the card in exile as the source even though it doesn't exist yet?

Additionally, assuming I can choose either object as my chosen source of damage, does the line “a source doesn’t need to be capable of dealing damage to be a legal choice” open the door to a “gotcha” if the player chooses the wrong source to prevent? Or do we just assume they meant the correct one?

The Kozilek's Return in the graveyard is the source of the damage, which renders the rest of the questions here basically moot.

As for the question of “gotcha” moments, those aren't something we want to encourage or enable, but thankfully that's not going to be something you need to realistically worry about in this scenario. It's just not going to happen.