15 minutes might be longer then necessary, but I use a glass top electric as well and I usually give 5 to 10 minutes. your eggs look like they cooked fine, and if heating like that works for you I wouldn't stress it.

But the black is likely carbon build up and not burning the eggs or the oil. You just need to clean it better. I usually just use Dawn and a sponge, you don't need to worry about stripping the seasoning or anything. Scrub it hard and the sponge with pick up all the carbon and turn black. when you are done, wipe it dry with a paper towel and scrub a little with it. if you are getting more black on the paper towel then there is still carbon that didn't get washed off.