Hi, no, not normal. But since the duck hatched itself out, maybe it's just a fluke...it's not as if you rushed the hatch and have a premature duck on your hands. Is there a yolk sac attached to the duck as well, like a yellow "belly button"? You'll need to make sure that the cord and the yolk sac don't get infected. I would go to a nice supplement store and buy some colloidal silver or nanosilver solution, and use fresh cotton swabs to lightly swab the cord/yolk sac with the silver solution every 6 hours. Some people use other products but the silver is the cleanest and most effective product to prevent growth of bacteria/fungi/viruses.
Keep the duck on clean towels and never let it lie in its poop, to prevent infection. The duck should absorb the yolk sac and the cord should drop off within a few days.
It's fine, sometimes they kick out before the final fibers dry and disconnect. Just make sure the shell doesn't snag on anything causing the cord to rip before its ready to fully disconnect.
Edit: I'm not sure what you were asking at first. I looked up what an unabsorbed yolk looked like and this does not look like that. Its just the cord leading to a tiny bump where the stomach is. No, there is no yellow attached onto his stomach, it is just that umbilical cord coming out.
I have him resting on a damp washcloth in the incubator and he still seems to be lively, chirping and looking up at me.
My incubator is just a styrofoam cooler with a lamp above it and some wet rags.
Could I expect more problems with the remaining ducklings that hatch?!
Another one of them is very close to busting out of his shell.
It appears things may not have been as bad as I originally thought. The umbilical cord looking thingy is barely attached to where his stomach is anyways. There is some gunkish looking stuff that came out of the egg with him, but he is still chirping and moving around okay. Doesn't appear to be bleeding or anything along those lines. I hope he is alright!
As I had mentioned, the cord was barely hanging anymore. I checked again and he was free from it. No blood or holes anywhere. He is still in the incubator watching his brothers and sisters crack out of heir shells!
So its safe to leave him there to rest for a while. Even if he's on top of other eggs? I have a home made cooler incubator so there isn't a whole lot of room.
very exciting, hope all goes well for the rest..the first will help the others hatch as they hear all the noise they will be eager to get out and see whats going on.