No, I think your definition of politics is too restricted. There's no need to support opposition of any politician to be political. If it were, anarchists wouldn't be classified as political, which is absurd.
That's true of all words, so why not just stop talking. No, because there is an average meaning which most people will agree with, something to do with making decisions that effect groups of people. See a dictionary or an encyclopedia.
No, I think your definition of politics is too restricted. There's no need to support opposition of any politician to be political. If it were, anarchists wouldn't be classified as political, which is absurd.