Where can I watch Cartoons and Movies in Chinese for free?

youtube

Try Tencent Video, iQIY, Youku, they all have some videos you can watch without paying for the VIP

I use olevod.com

basically you just google the name of the drama/movies and add "线上看“ (means watch online), you can get tons of resources.

Try https://www.bilibili.com/ . There are tons of great videos, movie clips and free Chinese animations! 

You can download the app: bilibili. There are lots of TVs and videos on it. You can learn a lot for free. 

cooldrama

you can download some APP like: 人人视频、Bilibili、韩剧TV

www.bilibili.com

or 

CCTV节目官网_央视网 

here is the official TV show website  of China