Feed them chick starter.
So up to three days without food, but it's better to have it available immediately, the same goes for water. If you have it available put a little apple cider vinegar in their water, it's okay if you don't though. As for the stickiness I assume that will go away as they dry more and preen themselves. I noticed when I hatched ducklings last year their feathers would stick to my fingers a little but not because they were sticky, just because the where getting thicker down in and the baby fluff was starting to shed.
Also I'm a little confused as to whether you mean the brooder or the incubator? Once they hatch people usually leave them in the incubator for 12-24 hours to strengthen and dry. After that they go into a brooder with food and water, you have to show them where the food and water is. This is done by dipping the tips of their beaks in each substance.
Chicks are usually kept in the brooder until they are 6 weeks old, that way they have pretty much all their feathers and depending on your climate will be able to keep warm.