It wouldn't hurt to give him a little clean up, a warm damp sponge or cloth, then give him a little dry with paper towels and put him under the heat plate to dry. Just ensure he's kept warm until dried fully.
I think where the down is crispy, he may feel irritated and that may be why he's...
You're doing all the right things
Bear in mind that he is younger than them, and may not show much interest in food or water until he's a couple days old. Keep encouraging him, and he should gradually gain an appetite and some energy
Picture?
It's likely not an issue, some do have "fleshy belly buttons" where there's a stump of umbilical cord left. Depending on how much is there, it may not even be visible once fluffed up. A photo would help
So you have two already hatched in the incubator who want to come out? 48 hours...