Chancellor
He was elected as President of the Republic of Germany.
In feudal Germany the village leader was called the Burgermeister. The title of the Burgermeister often translates into English as mayor.
Yes. The German Chancellor is, indeed, a publicly elected official.
Prime Minister
He became the leader of Germany on 30 January 1933.
Washington DC is governed by an elected Mayor and an elected city council.
Angela Merkel is the Chancellor. She is the leader of the German government, but not the leader of the country. Germany has a president, currently Joachim Gauck.
"Kaiser" which actually originates from the Roman title of Caesar.
It was the Title used by Adolf Hitler for that purpose. Germany still uses the title, but the translation as "Nation Leader" is misleading.
That was the title Hitler was given after he became leader of Germany.
Germany has a Prime Minister who is also known as the Chancellor. It is better to call the leader the Chancellor. So... Chancellor is the title of the leader.
Democracy - the power of the people - he was elected. Then the elected members decided to make him leader for life.