Lilibet.
No elizabeth did not have children she was what some people call her 'The Virgin Queen'
When Elizabeth II was a small girl, Queen Elizabeth the Queen Mother called her 'Lillibet'.
Mary Stewart, Queen of Scotland's cousin Elizabeth I of England never had a baby. That is why Elizabeth was known as the 'Virgin Queen'. Elizabeth I was never married and never had a child so she did not call her baby anything because it did not exist.
It comes from Queen Elizabeth I, the "virgin" queen, of England.
Susan
The parents of Queen Elizabeth II were King George VI and Queen Elizabeth (formerly Elizabeth Bowes-Lyon). When the King passed away, his daughter succeeded to the throne and became Elizabeth II in 1952. Her mother then stepped aside and became the Queen Mother. (Elizabeth I reigned in the 17th Century - The Queen Mother was NOT Elizabeth I.)
bessy
Liz 10
Elizabeth I was never referred to as the Pirate Queen. That title was given to Grace O'Malley of Ireland, a notorious woman pirate who lived during Elizabeth's reign.
Corgi
In formal circumstances, "Your Majesty". I do not what she is called by them in private.
The princess is any female relative of the king or queen; for example princess Margaret was Queen Elizabeth's sister.