1. The proc is Shadow damage.
As such it can benefit from shadow enhancements, especially Ebon Plague. My average drain came to about 2.9k as an Unholy DK.
2. There is NO internal CD on the proc.
Or if so, it is less then 2.7 seconds, since I watched it go off on two consecutive melee swings.
3. It is about a 15% proc rate.
This number determined by just standing and auto attacking a dummy for a solid half hour.
4. It DOES proc off of skills
When going all out, the proc occurred roughly twice as often for me (procing roughly the same number of times as BCB, which is 30% chance on melee swing with a small internal CD), going so high as 45 procs within 100 melee swings. It seems to be quite random as the numbers tend to vary wildly though. While I haven't tested enough to prove it, I highly suspect it can only proc off of physical hits (it only makes sense).
5. The proc CANNOT crit.
Not once did it ever crit for me in my extensive testing.
6. The proc CAN miss.
It appears to be regarded the same as any other spell and can miss depending on your spell hit or be partially resisted.
7. Spell power does not increase the proc's damage.
Can't be as sure with this one, since the only spell power I could get was a 46 spell power food, but I found absolutely no noticeable increase in the proc's damage after eating.