Yes, because she's the head of state. Australia could vote to get ride of the monarchy whenever they like, so there's no point playing the victim card.

YES

The Australian Constitution requires them to swear or affirm their allegiance to the Crown.

Yes. But, after all, as the "Bruces" say in that Monty Python skit, she's a good sheila and not a bit stuck up.

Yes. The Oath or Affirmation is in Section 42 of the Constitution and therefore, unless amended, will stay with us. The affirmation is:

I, A.B., do solemnly and sincerely affirm and declare that I will be faithful and bear true allegiance to Her Majesty Queen Victoria (now Elizabeth the Second), Her heirs and successors according to law.

If Australia becomes a republic, Section 42 of the Constitution will be amended accordingly. It doesn't bother anyone so it will continue while the Queen of Australia is the Head of State.