That is not possible. The use of Cloudflare nameservers has always been a requirement to use Cloudflare Registrar.
No it doesn't. It isnt permitted on any subscription. You are confusing custom nameservers with something that it is not. That feature allows you to apply vanity names to Cloudflare nameservers, but you still will be using Cloudflare nameservers.
I had a similar issue with my domain, drywallkingston.com (Drywall Kingston), and switched to Cloudflare for DNS-based renewal of Let's Encrypt wildcard certificates. Their API is straightforward, and I haven't faced any issues since the transition.