Can I put fanfictions I have written or the story of original characters, that are connected to already existing piece of media, I have written about in my portfolio?

Of course! Any piece of creative work is appreciated. Your portfolio is supposed to show your creative mind and show creative work that's connected to multiple creative solutions.

Keep in mind that creative writing isn't a huge part of the study. Make sure to have some technical work in your portfolio as well. This isn't only for your interviewer but also for yourself; as either a designer or artist, creative writing is only a small and early part of the development process.