Is making youtube fan content for a cartoon/video game/etc and monetizing the video illegal?
Really depends on what you are talking about. If you are showing clips of cartoons and telling your opinon on it kinda like Cinema Sins or Cinema Wins then no that would not be illegal. If you make things like music videos, then yes that would be illegal. Playing games like Markiplier is not illegal and making animations of your own playthrough is not illegal. If you just animate a game and put it up then that is probably illegal.
You need to read the Youtube rules if you have not done so already because it might give you a deeper understanding.
Hope I helped at least a little and good luck with your channel.