If a guy who is not a hemophilia patient, but has an uncle (mother's brother) who has the disease, can he carry the gene?

No. No, he cannot. The gene for hemophilia is on the x chromosome. Since a man has only one x chromosome, if he had the gene, it would express itself. That means he would show sings of hemophilia. There are only female carriers of the gene. Males will either have the disease or won't have it.