Bush had a ton of these types... not just Dick Cheney, but Rove, Wolfowitz, and a bunch of others hated by the left. The left is good at personalizing a battle, I think it's an Alinsky tactic.
True. I think everybody does it. However, the left are far more organized, clever, and avid about staging protests: getting people to march around, yelling and holding up signs. They have whole constellations of little non-profits dedicated to any issue you care to name (funded by...?)
So far as I'm aware, there isn't anything of the sort on the conservative side.