What's left of the British Empire is no longer a monarchy, technically. The government is run as a democracy, although the British have retained the royal family anyway, and the Queen has many duties. They are mostly ceremonial, but she (or any other reigning monarch) has quite a bit of power enshrined in law. As a matter of custom, she rarely meddles in the working of Parliament. But she could if she wanted to.
As the current monarch of the United Kingdom, Canada, Australia and a bunch of other countries that have her on their money, the Queen enjoys something known as sovereign immunity. In a nutshell, sovereign, or crown immunity as it is sometimes known, means that the Queen is for all intents and purposes above the law. So does this mean that the Queen could just up and kill somebody if she felt like it, all the while getting off scot free? In theory, yes, absolutely.
Queen Elizabeth holds both sovereign immunity and diplomatic immunity. But that's only the first layer of immunity the Queen enjoys. There's an entire maze of laws and customs that would prohibit law enforcement from taking any action against the Queen, which you can read about at Today I Found Out.
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