How does the Boston Tea Party show that American colonists supported the following statement?
it is in separably essential to the freedom of the people and the undoubted right of englishmen that no taxes be imposed on them, but with their own consent, given personally of by their representatives."
This statement is saying that only American colonial assemblies (elected by people in the colonies themselves) can tax Americans. This is because American colonists were not represented in the British Parliament. The Boston Tea Party shows support for this because it was a protest against taxation.
The Tea Party was a protest against a tax on tea that was imposed by the British Parliament. Even though it would have reduced the price of tea, it was resented because it was imposed by the British Parliament rather than by an American assembly. Because of this, the Tea Party (like this statement you give) is an example of the idea of "no taxation without representation."
what about for colonial boycotts, committees of corespondence, gaspee incident, and stamp act congress?