Animation became associated with kids once television took off as an entertainment medium. Networks wanted shows that would appeal to kids, and animated cartoons would often fit the bill perfectly. Some of the more business-minded animation producers like Paul Terry (Mighty Mouse amongst other cartoons) saw the profit potential and sold their cartoon catalogues to be broadcast on TV. This trend gave rise to the cultural institution of "Saturday Morning cartoons" that would, forever onwards it would seem, be animation's bread and butter in America. I can't go into more detail as I don't have my library in front of me, so I welcome anyone who wants to go into greater depth.

In answer to your second question, before this time animation was designed for a more general audience. Many early cartoons contain behaviors that are not strictly kid fare (drinking, lecherous behavior, not to mention the copious violence). Many studios even made cartoons to be used as educational films for soldiers during WWII. Disney in particular was more interested in what was possible with animation rather than what would appeal to just children. Look no further than experimental Disney movies like Fantasia or some of the more frightening sequences from Snow White and the Seven Dwarves or Pinocchio. By the mid-1950s, he would adopt a more paternal persona and lean more into the trend of children's programming, largely in an effort to promote Disneyland.

I know this is ask historians and this may not be allowed but if anyone is interested my father in law is Richard Reitherman, son of Woolie Reitherman one of Disney's Nine Old Men. Richard is extremely knowledgable about his father's work, intentions, and the inner workings of Disney in its early years. If anyone has questions i can relay them. Again if this sort of thing isnt allowed i can remove this post.