Hi, I'm a huge otaku [just got back from an anime con in fact] and what do people mean by 'the anime world' anyway? To answer your question no, you cannot be physically teleported into another world. There is alsral projection, but that is not physical. You could use your imagination and imagine yourself in your favourite anime, but there is no magical world where Inuyasha and Naruto hang out or whatever the 'anime world' is. Anime is a medium, like saying 'movie world' or 'cartoon world'. Sorry if I came across mean, you're not the first person to ask about being teleported to the 'anime world' and I've always wondered what people meant by 'anime world'. Is it like toon town from Roger Rabbit?
Absolutely! Learn about animation and read how to guides online. Make a japanese style cartoon of yourself in adobe flash or whatever program you like. There, you're in the anime world. No magic needed for this.