Yeah the baby can burn her eyes if she hits the heat element just right. I would probably take her out. But that is up to you.
As far as the sticky stuff on her, you can wash it off if you like, but as long as it's not covering her eyes or anything, I would just leave it. I sometimes take a hand towel or washcloth and kind of 'buff' the chicks that are really sticky. Eventually it comes off by itself. Chicks that are with mama hen use her feathers like a hairbrush, that's why they look so fluffy when they are brand new. I have actually thought of getting a baby hairbrush to 'poof' them up a bit, but the towel works just fine. I only do that cause that pink skin makes the older ones peck sometimes.
As far as the sticky stuff on her, you can wash it off if you like, but as long as it's not covering her eyes or anything, I would just leave it. I sometimes take a hand towel or washcloth and kind of 'buff' the chicks that are really sticky. Eventually it comes off by itself. Chicks that are with mama hen use her feathers like a hairbrush, that's why they look so fluffy when they are brand new. I have actually thought of getting a baby hairbrush to 'poof' them up a bit, but the towel works just fine. I only do that cause that pink skin makes the older ones peck sometimes.