In that case, I can answer this question:I’ll have to get one of him in the morning. But here’s GFF picture. He looks like this hen but much bigger.
He definitely has the barring gene.He’s a turkey head. I’m not sure if his coloring would be considered barred but he looks barred
I would say he is "barred" because he has that gene. Some other people distinguish "barred" and "cuckoo" based on how tidy the barring it, and I don't know which one they would say.
But either way, if he looks like that pictures, he definitely has the barring gene, so his chicks should have white barring, and he definitely has the genes to produce chicks that are black all over (dominant over most other chicken color genes) with the white barring over the black.
So with most hens, I would expect him to sire chicks that look like himself: black with white barring.
You have several chicks matching the light color of the mother, and no dark chicks from that pairing, right? That definitely shows the mother has a dominant gene of some sort. Dominant White can certainly do that, and so can Blue. But they aren't looking as white as Dominant White should be, and they are looking too light for what Blue usually is, so I agree with you in being puzzled about what is going on genetically (basically, for your question in the first post, I don't know the answer either.)
The rooster could have one copy of the barring gene (gives it to half his chicks) or two copies (gives it to all his chicks), and we won't know that until we see a photo of him. The appearance is usually a little different for chickens with one vs. two copies of that gene. But either way he should be producing black-based chicks, not lavender or recessive white (because both of those are caused by recessive genes, which he is not showing and should not be carrying either.)