If the Easter egger ends up laying blue, absolutely put her with the Mosaic. Otherwise you won't be able to tell her eggs apart from the Ameraucana eggs. If she has muffs, I'd honestly keep her with the Mosaic no matter what she lays, since you'll probably be able to tell her chicks apart at...
Well, usually within a day or two. Mine take a few hours to darken and lighten to where I can tell them apart. But yes, Dark chicks if bred properly will be female and light ones will be male. If you use the wrong hens, they all will hatch dark though
Has to be a mosaic rooster if you want to...
You can always keep the Ameraucana you like and the Mosaic your husband likes. Put the Mosaic hens and light skinned hens with the Mosaic, and the Ameraucana hens and dark skinned hens with the Ameraucana.