Is queen Elizabeth II a citizen of the United Kingdom, Canada, Australia, etc?
If not, what about the rest of the royal family?
No, she isn't.
A citizen is:
A legally recognized subject or national of a state or commonwealth, either native or naturalized:
A supreme ruler, especially a monarch
It would be odd to describe the Queen as ruler and subject to herself. As to the Royal Family, they are subjects of the Queen, but retain citizenship of the country of origin, unless naturalized
It was not unusual to naturalize husbands (and also sometimes wives) of members of the British Royal Family. [...] 49 & 48 Vict c.1 (1885): private act naturalizing Prince Henry of Battenberg future husband of Princess Beatrice, daughter of Queen Victoria.