To help answer this question you should draw a pedigree and complete a punnet square.
From this information we can assume that the mom has two color-blind alleles because 100% of her sons are affected.
It is easier to answer question #2 first. It is clear that this condition is X-linked because all of the sons are affected and none of the daughters. Why does this matter? Look at the punnet square. Remember males are XY and females XX. Only a male can give a Y chromosome meaning their X chromosome comes from the mom. If the mom gives an affected X chromosome then the son will have a 100% chance of having the phenotype.
Now let's answer question #1. 100% of the sons are affected so let's assume that the mom is homozygous for the trait because they all got an affected X chromosome. None of her daughters present with the phenotype so even if they are carriers of the gene they do not have the condition. This makes the condition recessive.
Now #3. Remember our discussion about male and female genotypes? Since women are XX the only chromosome they can pass to gametes is an X. Males have XY meaning they can either pass an X or a Y to their gametes. Sex of a child depends on if the male X vs Y gametes fertilize the female X gamete.
Hope this helps!