well japanese do speak fast, but to them the is the normal pace. just like english speaker , to japanese they speak really fast , but for us that is just a normal pace.
anime is a good way to practice your listening skill. but be warn that lots of format use in anime are considered rude on daily basis. So just learn proper japanese, and if you ask locals to speak to you slowly , they would gladly do it, so don't be afraid to say/request to speak slowly and properly.
you will get use to it, after a living in Japan
well good luck on your japanese studies