First time byc first time incubatorer
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Newly hatched chicks can live a day or two without water or food. I leave mine in there at least 12hrs minimum, even a little more. It is bad to take them out before they are dry. They should be dry in a few hours. Some take longer than others. I've had some pip and hatch up to two days later. Be patient. I usually dont help them. Just keep the humidity a little higher maybe 60 to 80 %. Let nature take its course. Have fun and enjoy them.
- "Pesky Polands!"
It can take up to 24 hours for them to hatch after pipping. Some less time some longer, each chick is individual and there is no set time. I leave mine in the incubator untill hatch is done or it looks too full, usually about 24 hours.
The little red bit sounds like it could be an umbilical issue. Either unabsorbed yolk, part of the cord or part of its intestines coming out. Don't pull anything in that area as it could cause more damage. Once she is dry and fluffy you can take a look at it. Hopefully it's just a bit of cord and should dry up and fall off of its own accord. If not you need to keep the area as clean as you can so it does not get infected.
Here is a lovely article on incubating and the hatching process ~http://www.backyardchickens.com/a/hatching-eggs-101
Good luck with the rest of your hatch