Privacy

This very much dependent on which registrar you use and what TLD you choose. Most of them have at least some ID requirements as they're required by law to provide it to the TLD registry.

Domains registered for individuals typically hide your personal info from public WHOIS databases, but comercial use usually requires public disclosure.

Some TLDs enforce identification requirements; and will even lock your domain until it can be verified. Here's info on .ca domains.

Some registrars will allow you to register anonymously; but they typically register the domain in their own name then enter into a contract with you, giving you control of the domain while they retain legal ownership. Njalla is the big name there; from the founders of The Pirate Bay.

You can find some anonymous one but they end up owning it and just give you a contract of full management of it.

I found that they ask for my name, phone number, and address.

Are all of these required fields?

yes, they do, I am also fed up with this, but if I am not wrong, it is required cert giving organisations, they sometimes even do video kyc.

you can try to find a good free subdomain, theey would just ask for a email, but that would be a subdomain, and nothing more

You can fill in any random information you want. I have domains that were registered over 10 years ago that were registered to some random credentials. But if you want to sell such a domain in the future or transfer ownership of it somehow, this decision can cause you serious problems.