Yes, it is very easy. Yes, pay by bitcoin. Many registrars offer that. Or pay by cash or by prepaid card.
There is no privacy if the money-trace is aiming at you.
The registrars answer to police or whoever is pretending they are police more frequently than you think. Nobody is waiting for court decisions.
Just with bitcoin be sure you do not mix the money with other coins that can doxx you. Or use the mixer to be sure.
If you talk to God, you are praying; If God talks to you, you have schizophrenia.