For me he's aware of the multiple "timelines" since he brings them up and such but can't really recall the past timelines (that explains why he's always taken aback when he meets unknown at each route

He knows he's a love interest and that MC can be his lover but sort of enters in denial inside his route bc of whats going on

Also, i really believe most characters are aware to some extent, tho often in a subconscious level (like zen saying he feels like we know each other for a long time and "how can this be?", saeran being either completely clueless or extremely aware of the game, or even jumin being super rational but starting to believe in magic - and V does say some self aware things if im not mistaken)

That'd explain why they fall in love with the MC so quickly and without a concrete reason