Black residue inside frying pan
What you are seeing is almost certainly a form of firescale, and it should be completely harmless.  If the discoloration bothers you, you can try to remove it using the aforementioned Barkeeper's friend or a mixture of boric acid and denatured alcohol (which are non-toxic).

With regard to cooling off the pan, you should never put a hot, empty pan into a cold, wet sink: The temperature change can cause the pan to warp.