Yes, their daughters should lay blue eggs.I have 2 EE in my flock, one Rooster, one hen...I was told they are Blue Amerucauna Rooster with Isabel Amerucauna Hens. They both hatched from blue eggs. My hen just started laying and she lays lovely little blue eggs.
...will they have blue eggs if they are from the birds they say they are from?
With the current rooster, if you hatch the brown eggs from your current hens, their daughters will most likely lay green eggs. (Assuming you were told correctly about your rooster: if both of his parents are Ameraucanas, he SHOULD be pure for the blue egg gene, so all his chicks will inherit it.)All of my other girls lay brown eggs, if they bread with my rooster will they have a mix of eggs?
Blue eggs with a brown coating on the outside look green, which is why the daughters of the brown-egg hens will lay green eggs, rather than actual blue ones.
Beard is dominant.Will all of his offspring have a beard, is that dominant?
That means you cannot tell by looking at your rooster whether he has two copies of the beard gene (so all of his offspring will inherit it) or only one copy of the beard gene (half his offspring will inherit the beard, and the other half will not.)
If both of his parents really are Ameraucanas, and have the genes Ameraucanas are supposed to have, then your rooster will produce only bearded chicks (he has two copies of the beard gene, every chick gets one copy of the gene, because it is dominant you see a beard on every chick, no matter whether their mothers were bearded or not.)