What are all the sex-linked traits and why are they so?

Yes, the father of a color-blind daughter must be color-blind himself (at least in the case of traditional color-blindness).

Color-blindness is carried on the X chromosome and is a recessive trait. In order for a female to be color blind, she must get a recessive X from her mother (who could be color blind or could be heterozygous), and a recessive X from her father. Since the father only has one X chromosome, it has to be recessive. If the father had a dominant gene for color-blindness (meaning he was not color-blind), then he would pass that to his daughter (again, since he only has one to pass on), giving her at least one dominant gene and hence, not color blind.

It's much easier to follow if you draw out the genes. Females have two X chromosomes, while males have an X and a Y. Traditional color-blindness is only on the X chromosome, so only draw those potential offspring.

There are too many sex-linked traits to list, but hopefully this helped with colorblindness as an example for how X-linked traits work.

They wouldn't have to have a colour blind father or mother. There parents probably have the same chromosone for colour blindness but it wasn't activated in their genes.