According to the tool Lynda gave you and with the info given, the most likely relationship to your daughter would be a great-uncle or half-uncle. You assume that the matching people must come from your side because the race is the same as yours. That may not be the case, but you have not given enough information to understand why you say that. We don't have any information about your mother, your father, your siblings, or why you say she doesn't have any cousins. One of the easiest ways to gain information about these people's relationhip to your daughter is for you to take a DNA test and then see how your results compare to your daughter's. You may be surprised to find the relationship! You may have an unknown half-brother! Or one of your parents may have an unknown half-brother. Considering the info we have, that is possible. However, it is possible that these people are related to her father, even if they are a different race, if they are half-siblings to someone.
As to the other question, most likely reason that the #1 male's dna is twice as much as the other male's DNA and his mother's DNA is probably because the #1 male and the unknown female are half-siblings. It is not unusual for a parent's and child's amount of DNA to be the same in relationship to another person's. I think that is simply because of the way DNA is tested -- NOT because they are the same distance in relationship. I find this quite commonly in my DNA comparisons with my mother's and my DNA relationships. If the person is far enough away, my mother and I share the same segment and same number of cM with that other person. I have to admit that 488 cM is a lot of DNA. Maybe a DNA expert can pipe up here with an opinion.