Don't all Easter Egger's lay green eggs?
This topic gets really messy because there are a lot of misunderstandings about what an EE is. The original blue egg layers were discovered in Chile. When they were originally exported the guy that introduced them to the rest of the world mixed them with different chickens that had pea combs, no tails, and growth on their faces so they were mixed up from the start. The original green or blue egg laying breeds were developed from these barnyard mix chickens. Some people think the EE's were made from these original breeds. The opposite is true. You can make an EE from one of those breeds but you don't have to.
Some people define an EE as a pullet or hen that lays a green or blue egg but is not a specific breed. Since a cockerel or rooster doesn't lay an egg how can you get an EE male if you use that definition? Some people define a chicken as an EE if its mother, grandmother, of one further back in its lineage laid a blue or green egg even if the hen in question lays a white or brown egg. Some use other definitions. I said it gets messy.
There are two genes at a certain gene pair that control whether the base egg shell color is blue or white. Since blue is dominant if just one of those two genes is the blue eggshell gene the base color will be blue. Brown or green pigment on the egg shell is controlled by other gene pairs. Brown or green eggs are simply brown pigment on top of the base white or base blue and is generally applied in the last half hour before the egg is laid. Think of it like this:
Base white + no brown = white egg
Base white + brown = brown egg
Base blue + no brown = blue egg
Base blue + brown = green egg.
There are a lot of gene pairs that influence the shade of brown, that's why you can get so many different shades of brown or green.
What I have read is that crossing a blue egg layer with a brown egg layer would give you a green egg layer. Is this true 100% of the time?
No, not 100% of the time. A blue egg layer may have two blue eggshell genes at that gene pair or they may only have one blue eggshell gene. Remember blue is dominant. If one of the parents has two blue eggshell genes then they will always give a blue eggshell gene to their offspring and any pullet will lay a blue or green egg. But if the blue egg layer only has one blue eggshell gene about half the female offspring will get the blue eggshell gene and half will not. So a blue egg layer does not always give you a blue or green egg layer.
Does an Amerucana mixed with anything else become an Easter Egger and lay green eggs? For example, if I breed this rooster (my only rooster) with my ISA brown hens and my Black Australorp hens, will all the babies be Easter Eggers and will the hen version of those babies lay green eggs or do they have a 50/50 chance of laying brown eggs?
If he is truly an Ameraucana rooster then by breed definition he has to have two blue eggshell genes at that gene pair. So yes, when crossed with those hens you will get pullets that lay green or blue eggs. Almost certainly green with those. The problem with that is that some hatcheries sell what they call Ameraucana but they really aren't. Some of them sell EE's and call them Ameraucana. Since roosters don't lay eggs you don't know for sure that he even has one blue eggshell gene. The only way you will know for sure is to hatch some eggs and see what color of eggs the pullets lay.