Quick answers to your three questions:

1. You still need DDNS if your IP is dynamic — the domain has to keep pointing at your changing home IP. (If your ISP gave you a static IP, you don't.)
2. Your DNS/domain provider only resolves the name to an IP; they can't see the stream itself — it's end-to-end HTTPS. They could log which hostname is queried, not the content.
3. The unreliable part you want to fix is the free DDNS, not the domain.

Full disclosure: I operate DNS Beacon. It does bring-your-own-domain + a reliable DynDNS2 endpoint + free auto Let's Encrypt on the free tier, GDPR-compliant German operator. https://dnsbeacon.com

Porkbun + this combo works well together.