Queen Elizabeth II came to Korea on April 21st, 1999.

1. Queen Elizabeth Two
2. Queen Elizabeth the Second
(How do we read 'Queen Elizabeth II? #1 or #2?)

Her name and title are correct as you've written them in your sentence. They are pronounced as in your example #2.

You can also see Queen Elizabeth II.

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To properly read "Queen Elizabeth II," you would read it as "Queen Elizabeth the Second" (#2). The "II" represents the Roman numeral for the number 2, indicating that Queen Elizabeth is the second monarch with that name in the recent history of the British monarchy.