I’m not familiar with that cross so can’t help you much there. The Speckling (mottling) is a recessive trait so it will not show up on the first generation. The chicks should all be red, I can’t go beyond that.
In genetics there are typically two genes at any point on the DNA with both males and females. As always with chicken genetics there are exceptions, the sex linked genes, but those are pretty insignificant in this case so to simplify let’s forget about those. Each parent gives one copy from that gene pair to all their offspring. Some of those genes are dominant, some recessive, some partially dominant, some only act if another certain gene is present. It can get pretty complicated pretty fast.
But to answer your specific question, it does not matter which parent the gene comes from. The hen does not have more influence than the rooster. Ignoring the sex linked genes the rooster does not have more influence than the hen. What matters are what genes the chick inherits and how they work together, not which parent the genes come from.