We actually have no problem cooking eggs in our CI skillet. We never did the baking thing, but we do always give it a shot of olive oil when we cook. Acutally, we heat it up, spray the oil (we have a mister), and then let the oil heat up a little more. Then, and only then, do we put anything in it to cook. I do eggs, brown meat, make quesedillas, sautee veggies, and lots more in it. I love it!!
Usually I just wipe it clean after cooking with a paper towel, but once in a while something burns and gets stuck. I know some people will turn their noses up at this, but in those instances I do rinse it and use the rough side of the sponge to get the stuff off. After I wash it, I heat it up again, spray with oil, and turn off the stove, leaving the hot oil to soak in.