The rules claim it should be as realistic as possible, is it however possible to include smaller passenges in which the character experiences psychological phases or other kind of unreal encouters to emphasize the well being of the character or is it not allowed?

That’s completely fine. You can absolutely include psychological moments, surreal sequences, or other atmospheric elements to help show the character’s mental state or build tension.

Just make sure that if you create or expand on scenarios, they’re still grounded in what’s known or believable based on real information about that person. It should feel like something that could have happened, not something totally disconnected from reality.

A great example of this is Jeffrey Dahmer, he was completely isolated, a loner, and a "class clown" in highschool. If you wanted to make a segment of the game talking about his past, just make sure it's beliveable based on how the serial killer actually was.