You have configured Cloudflare nameservers and our nameservers on your domain. As the red warning banner in the domain checker says: don’t use multiple DNS providers at the same time.
If you want to use Cloudflare on your site, make sure you ONLY have Cloudflare’s nameservers. If you want to use our nameservers, then remove Cloudflare’s nameservers.
And no, you don’t need to keep using our nameservers to keep using our hosting. If you want to use Cloudflare with our hosting, you should still only have Cloudflare’s nameservers.
One caveat if you are going to use Cloudflare: if you setup a new subdomain, you will need to create it in our panel (so the website is setup), but also setup a DNS record in Cloudflare so the subdomain is actually routed to our servers. You can setup an A record and point it to your Website IP, or setup a CNAME record and point it to your base domain.