the answer to pretty much all of these is that the champion will get their extra turn, but freyja's passive grants priority so the opponent will get their turn first, after which whisper/nekhret/relentless/etc. will go.

in valkenan's case, i expect he will simply ignore freyja's passive. i'm not entirely certain whether he'll even trigger it in the first place (from what i've seen, similar effects seem to be handled on a case by case basis), but even if it does, his a3 seems to be able to get around any and all effects that would ordinarily prevent the targeted champion from dying. i doubt this will be any different.

Ok but we're not sure then about that first part? Because what if the Champ who gets the Instant Turn uses an ability that grants Extra Turn? Or is wearing Relentless themselves? Then what?

See how this can get really interesting/complicated?

extra turns act in the order that they were recieved, so priority would return to the opponent. the reason freyja interrupts the order is that due to the way the game functions, the extra turn she grants is considered to happen before the ability of her opponent.

we'll use whisper as an example. her a3 consists of 2 steps; first she attacks, then she gets an extra turn (technically 3 steps including the check for def down and weaken debuffs, but that's not relevant to this situation). freyja's passive activates in response to an attack, which means the effect takes place in between the two steps of whisper's a3, granting the first extra turn to whomever her passive affects.

full disclosure, i don't actually have freyja and this is all based primarily off my experience with rotos and how his passive functions. i would assume that freyja's ability works similarly, but it would hardly be the first time encountering inconsistencies in plarium obscura.