So, if I understand correctly re EEs about their genetics -- an EE hen that lays brown/pink eggs can still be carrying the blue gene and doesn't necessarily need a blue gene from an EE roo to still produce offspring that can possibly be blue/green egg layers themselves if they inherit a blue gene from her?
No. The gene for the blue shell is dominant over the genes for white shells. The brown 'coating' genes operate and inherit independently from the shell color genes. Brown/pink layers have no blue shell gene to pass on.
Probably a low probability but the offspring of at least one blue-gene parent can still grow up to be blue/green layers themselves and pass along the blue gene to their offspring too, albeit probably quite a diluted possibility?
The blue of the blue shell gene does not dilute over several generations. Birds with one copy of the blue shell gene can lay eggs that are just as blue as birds with two copies.
Or is the blue gene a dominant gene and always comes thru as either a blue, green, or olive egg?
Yes, it's a dominant gene. There are only two options for shell color genes, white or blue. Brown eggs have a coating applied to a white shell. Green eggs are the same coating, but applied to blue shell. There are over 9 different genes for the coating, and birds can have many of them at once. This is why there are so many shades of browns, from cream to dark chocolate.
I tried to follow the genetics of blue, white, brown egg layers on the Marans club website but I can't follow the +/o, allele, etc descriptors in figuring out what's going on. I never covered genetics in Biology in the '50's.
http://maranschickenclubusa.com/ A Review of Egg Color in the middle of the web page.