Under what conditions can Queen Elizabeth II create laws?

You sent me down a Wikipedia rabbit hole. I knew some of this, but not all.

For an appetiser, check out letters patent:

Letters patent are a form of open or public proclamation and a vestigial exercise of extra-parliamentary power by a monarch or president. Prior to the establishment of Parliament, the monarch ruled absolutely by the issuing of his personal written orders, open or closed.

They can thus be contrasted with the Act of Parliament, which is in effect a written order by Parliament involving assent by the monarch in conjunction with its members. No explicit government approval is contained within letters patent, only the seal or signature of the monarch.

Parliament today tolerates only a very narrow exercise of the royal prerogative by issuance of letters patent, and such documents are issued with prior informal government approval, or indeed are now generated by government itself with the monarch's seal affixed as a mere formality. In their original form they were simply written instructions or orders from the sovereign, whose order was law, which were made public to reinforce their effect.

For the sake of good governance, it is of little use if the sovereign appoints a person to a position of authority but does not at the same time inform those over whom such authority is to be exercised of the validity of the appointment.

As to your question about what the Queen can do, the standard answer is that Parliament is sovereign, not the monarch:

Parliament means, in the mouth of a lawyer (though the word has often a different sense in conversation) the King, the House of Lords, and the House of Commons: these three bodies acting together may be aptly described as the "King in Parliament", and constitute Parliament. The principle of Parliamentary sovereignty means neither more nor less than this, namely that Parliament thus defined has, under the English constitution, the right to make or unmake any law whatever: and, further, that no person or body is recognised by the law of England as having a right to override or set aside the legislation of Parliament.

A.V. Dicey Introduction to the Study of the Law of the Constitution (1885)

This was formalised in the Bill of Rights 1689 which declares that:

the pretended power of suspending the laws and dispensing with laws by regal authority without consent of Parliament is illegal

So she would have to get the rest of Parliament to agree to repeal that act to begin with. That act is shared with the rest of the Commonwealth realms, so that would be a major diplomatic feat. Here's New Zealand's version of the dispensing powers section, for example.

Not a parliamentary lawyer, but my understanding is the Queen's current standing is closer to that of the First Lady of the United States. She is her nation's official diplomatic hostess, with zero legislative authority.

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One additional minor comment. The Commonwealth includes a lot of countries where Queen no longer reigns. She's still the monarch of the 16 Commonwealth "realms", but there are a total of 53 states in the Commonwealth. The other states have their own presidents or monarchs.