Indeed, 1c, regardless of the velocity of the observer.
The speed of light in vacuum is constant and independent of the frame of reference of the observer or the motion of the source.jr2: Your example is based on a principle that sounds really weird and contrary to common sense, yet is demonstrably true.
Velocities are not linearly additive, which means you can't simply add the numbers together as you'd expect. If I'm driving down the road at 60mph, and I throw a baseball out the window at 40mph (relative to me in the car), and I throw the ball in the same direction that I'm driving, then you'd expect to be able to say that the speed of the baseball relative to the ground is 60mph + 40mph = 100mph. But this would be wrong! It's actually 100mph minus a tiny little bit, that little bit is because of relativity.
If you examine the math behind this, the effect ends up being insignificant at small, every-day speeds that we're used to, but very significant at speeds close to that of light.
Bob: I'm really not sure how to answer that exactly -- it would depend on your speed and trajectory around the black hole, the black hole's mass and angular momentum, as well as the position of the observer. It's mathematically too involved for me to be willing to try to go through, sorry.

I suppose what I can do is recommend looking at
this website that Astronomiya provided for me a while back during a similar discussion on black holes and relativistic effects. It's a really nice one and might help provide further insight.
