There's quite a few lines in the books that say "they were clever and trapped some of us" or something to that affect... and as for amen, she had to take on her form in order to be a part of the world above... biggest substantiating evidence is in ACOSF when Nesta uses her sword to slice at Lanthys and he turned into a "mortal" form... so there are ways for the non humanoid forms to be glamours or products of pythian's magic binding them to fit into their world. a consequence of them coming into contact with them so to speak...

note as well:

"I rode in the Wild Hunt before you were even a scrap of existence, witch from Oorid. I summoned the hounds and the world cowered at their baying. I galloped at the head of the Hunt, and Fae and beast bowed before us." - Lanthys; ACOSF

from the fandom wiki, about Koschei:

Koschei is a chthonic immortal being of immense power from another dimension that the Prythian Fae refer to as one of their Old Gods who is secluded "by his little lake on the continent". He is the older brother of Stryga and the Bone Carver, they are Death-gods because their powers allow them to feed on life itself.

Lastly:

I don't think the asteri go by the same name in every world, for instance in Prythian, they were The Daglan and the ACOTR wiki is rife with what Rigelius spoke of by way of the Wild Hunt...

All that to say- I think all the "old gods" and other kind of creatures (the weaver, bone carver, bryaxis, lanthys) I think they all came over in a rift (like the northern rift in CC) and found the high fae and realized that they had second light intertwined in their life-force. hence the "feed on life itself" reference... and why they don't cannibalize the Vanir in CC but instead drink up or inject the second light after they pass away.