I would treat it like is done with companion, so no choice for stickers, so every effect that put a sticker controlled by that player does not do anything during that game. 2/3

It is mentioned that if a player has not chosen stcks and resolves an effect putting one, can choose 3 randomly from the website. Imo this covers the case in which a player takes control of an effect which put stickers and does not play with stickers in the first place or RegREL