I am new to Cloudflare. I changed the name servers to my Cloudflare ones and a few minutes later my website stopped working. I also could not access my WordPress dashboard. I changed the name servers back and the website started working again and I could access my WordPress dashboard. I am not sure what happened.
I then used the WP Fastest Cache plugin to connect to Cloudflare. My site works OK for now. But I am not sure if I am getting the benefit of a CDN if my nameservers are still the old ones.