Can a student of non-science background pursue animation? Is it necessary to have a science background?

Not at all , you can say , it is the only unique stream which is a cup of tea for all , with different type of skills and not only academics . it counts your skills in any of the following creativity, photography, drawing painting, good understanding of color theory , acting skill, story telling ski

No as such it does not matter from which stream you have done your studies from, only thing that matters is that you have passion for animation.

no, it will not affect your choice because Animation is totally different stream

No, it is not necessary to have a Science background for pursuing Animation.