A CDN doesn't actually offer you to host websites. Basically it caches your website content, and can help you in improving the performance your visitors. Eventhough Cloudflare is the most widely used free CDN, there are other CDNs you might need to look : https://www.nets4.com/2020/07/free-cdn-providers.html
Ofcourse it is. Privacy is taken serious by people around the world. But you know it, companies like Google, Facebook will eventually get your whole data in some way.