That's fowl pox alright! It's nothing to worry about since the type they have, from what I can see, is the dry variety. If you want you can apply some neosporin or triple antibiotic ointment on the spots. I had a severe outbreak last year and all of my chickens and turkeys had it really bad, the only one that didn't make it was the one who got the pox in her eye and it became infected. No one else died from it but they all dropped like flies when they contracted Avian flu a couple months later.
Back on the pox though, there are two types wet and dry. Dry is the scabs that your birds have, wet is where they get these things that look like cheesy wads in their mouth. Wet pox is the type you have to watch for. Mine never got wet pox but I continuously checked inside their mouths to make sure they didn't have anything in their because it can block their airway if not kept under control.
I'm not sure about the eggs because mine weren't old enough to lay eggs then. Just let it run its course, it could take several weeks got it to completely go away but they should be fine if you watch them. Also go check out the threads on fowl pox there's a really good one but it's pretty graphic with the pictures of pox.