Questions about eggs

There are ways to tell who is laying what if you don't catch them in the act, but none that are really easy. Putting food coloring or lipstick on their vent that will color the egg shell seems to be a popular one, trap nesting (putting a door on the nest box that closes when a hen goes in it) / or if you see one in the nest, lock them in until they lay. If you only have a few hens, you may be able to tell their eggs apart to some extent since hens usually lay eggs that are pretty similar from day to day. If you want to incubate eggs only from certain hens you pretty much need to keep them separate if you have multiple hens laying the same color etc of egg.

There is no way to tell if an egg if fertile before it is incubated unless you crack it open. Here is a thread with pictures of fertilized vs not fert eggs https://www.backyardchickens.com/t/16008/how-to-tell-a-fertile-vs-infertile-egg-pictures

Most people call crosses like that, Ameraucana X pretty much any other breed or mix, Easter Eggers. If your rooster is a true Ameraucana, he should carry two copies of the Blue egg shell gene, so all of his offspring would get one from him, so all of his pullets should lay blue/green eggs even if the mother does not... (blue eggs are blue egg gene + white eggs, green eggs are blue egg gene + brown eggs, the darker the brown the darker the green, olive eggers are from really dark brown egg layers like Marans) If you roo is actually an Easter Egger himself he may still carry two copies of the blue egg gene, but some only carry one and some don't carry any.

There are some good articles on broody hens in the Learning Center you might want to check out. ie https://www.backyardchickens.com/a/guide-to-letting-broody-hens-hatch-and-raise-chicks and https://www.backyardchickens.com/a/encouraging-or-discouraging-broodiness-in-your-hens If you keep the broody and chicks totally separate you will need to integrate her back into the flock like she was a new bird. Depending on your set up, if you can keep them in small pens in the coop or even let her raise the chicks with the flock that usually works easier.

There is a wonderful article in the Learning Center that covers about everything on hatching eggs. https://www.backyardchickens.com/a/hatching-eggs-101 Know your incubator and what works best for the model you have (there are threads for most incubator types). Have an extra thermometer to double check temperatures.