I’m probably the last person who should give advice on how to learn Japanese since I don’t know the language, but I see no reason why you can’t learn from watching Anime. Since I know little about the language, it’s hard for me to make a differentiation between real life, everyday Japanese and anime Japanese, but I doubt there’s enough of a difference to destroy you potential to learn from it. I learned a vast majority of English from watching western media and later on enforced what little there was left with education. Sure, you’ll make mistakes that may be associated with whatever it is you’re watching, but with a bit of research and dedication you can learn from these mistakes.
Anyways, as someone who learned a language primarily from media, I recommend
this video since he pretty much echoes, in detail, my thoughts on language learning from media sources, text books, school and so on. Be warned though, the interviewer is a bit colorful with his language so if that sort of thing bothers you....well, now you know.
Good luck finding what works best for you.