The red one is definitely a roo. I think that Barred Rock is a hen, though--the neck feathers don't look very rooster-ish.
I raised two Barred Rocks out of 20 mixed chickens and because of their pinkish, large wattles and combs, I was terrified for months that they were roosters. They were all hens. It turns out sometimes Barred Rocks just have bigger, pink-er wattles/combs than other breeds of chickens. In my opinion, anyway.
I think it is a roo. And I think that it is a Barred Rock x Rhode Island Red cross. I had a RIR Roo and Dominique Hen's and some of the chicks that hatched ended up with very similar coloring.
The gold feathers mixed into his barred pattern probably would be from the Autosomal Pheomelanin (Ap) or "autosomal red" gene. Ap in silver penciled or silver laced roos causes golden feathers to leak through into the silver patterning. Since barred is also a silver based color it is likely that it is the Ap leaking through on your barred roo too.
So to be more simple, you are probably right about a gold or red colored parent being one of his parents. I could go further into the genetics of him but I'll refrain for now. Ask me if you want to learn more.