You should not brake check anyone, and if they hit you because you brake checked them, I am pretty sure it is considered your fault.
I don't have any story about a cop following me, but unless they have their lights on, they need to obey the laws. In the past, say, six months, the few cars that I have seen BLATANTLY breaking the 25mph speed limit where I live have all been cops. Ridiculous. No lights or anything either, going at what I would estimate to be at least 40mph through a residential area.