as far as i can remember yes, but it wasn't good, makes a lot of noise and hardly cools at all, i bought a bigger real cooler.

Yes, a round heat sink from Intel was included. I can't judge whether it is sufficient for the i7. We have never used it.

Yes, the custom fan for this CPU.

yes there is one, I have just installed the thing and the cooler is really bad, so you better buy a decent cooler ;-)