What is the ruling on watching a japanese anime in which the actors have "chakra" as a source of energy and who can use this "chakra" for special attacks like attacking with fire or water from their mounth's or constructing a wall from earth? If it is not permissible is the danger of quitting islam by watching these kinds of anime's?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

The Muslim should be keen on using his time in what is beneficial, and not waste his time –which is the most precious thing that he has –in watching cartoons that are destined for children.

As for the characters with supernatural powers in cartoon films, then what is permissible in our view is what does not include claiming some characteristics of Lordship or Divinity, such as the ability to revive the dead and the knowledge of the unseen, provided it is not magic or witchcraft, and provided it does not involve imitating Allah’s Creation, and so on.

What you have described in the question is most likely forbidden in the Sharee'ah, even though we do not authoritatively assert this; so it is better for you to leave it and stay away from it.

In any case, watching cartoons that contain anything that violates the creed is not Kufr, or going out of the fold of Islam, as long as the viewer does not approve of such violations.

For more benefit, please refer to Fataawa 95009 and 252502.

Allah knows best.