I. UK parliamentary monarchy today (docs 1, 2 & 3)

• Government buildings
Buckingham Palace : represents the executive power held by Queen Elizabeth II ;
Number 10 Downing St : represents the executive power held by Prime Minister Boris Johnson ;
Westminster Palace : represents the legislative power held by Parliament

• A democracy
In 1689, the UK wasn’t a democracy because the House of Commons was elected by less than 5% of the population : it was a restricted franchise.
In 1928, the UK became a democracy as women got the vote ; today everyone votes : it’s a universal franchise.

• The Queen’s role
In the UK, Queen Elizabeth II is the head of state. The prime minister (PM) is the head of government and holds power, he/she governs/rules. The monarch reigns but doesn’t rule, the queen has no real/actual power but she is a symbol of stability for the British people.
Canada, Australia and New Zealand are former British colonies which belong to the Commonwealth headed by the Queen. They are parliamentary monarchies with Queen Elizabeth II as head of state (she reigns) and their PMs as head of government (they rule/govern). So even if Canada, Australia and New Zealand are now independent states, they still have an English monarch.