It seems like the DNS for one of my domains is entirely broken. None of the records (A, MX, TXT, etc.) are working although the Cloudflare console shows everything fine. My other domain has not problem and works fine.
What feature, service or problem is this related to?
Yes, free users can raise account, billing and registrar tickets.
My guess is the wildcard is due to a suspension of your domain (maybe on the registrar side) and Cloudflare is redirecting to a page that says that, but something is broken so the page is not showing.