Question: How does a black hole rotate if time is dilated to infinity (e.g. stopped) at the event horizon? Note: this is relevant to this question, but different: [How can a singularity in a black hole rotate if it's just a point?](https://physics.stackexchange.com/q/103232/)

**Edit:** I am considering this from an external reference frame (e.g. like what we would see from Earth, or perhaps even an object somewhat close to the black hole, but not very close to its event horizon).

Answer: 
The statement "time is dilated to infinity at the horizon" is a (very imprecise) way of saying that the event horizon is a null/lightlike surface. However, as is clear from light-rays, being null/lightlike is no impediment to moving. In particular it is possible for a null/lightlike surface to rotate. (Just as photons move `despite' that "time is dilated to infinity on a light-ray".
A spinning black hole is characterized by a mass M and an angular momentum L. No further parameters, hence the question on the angular speed is not applicable.