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Very likely yes.
hes distantly related to you
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Only his father, as the genetic line indicators only run through the male chromosomes. Using a brother will not work, but you're talking about a very expensive test as it would be genetic mapping and not just establishing paternity. In a related interest story, genetic mapping was use to establish that an African tribe had Jewish origins.
Your aunt's husband is usually considered to be your uncle, but his brother is not related to you, so the brother's daughter is not related to you either.
Your wife's brother is your brother-in-law. Your brother-in-law's wife is not related to you, and the same applies to her sister.
Your husband's brother is your brother-in-law.
Your brother's wife is your sister-in-law, but her sister is not related to you.
Your mother-in-law's brother is your spouse's uncle, but is not related to you.
It depends on which "half" of your half-brother the nephew is related to. Your half-brother shares your father or mother, but not both. If your half-brother's nephew is related to the same parent you are related to, your half-brother's nephew would also be your nephew. If related to the other parent, he would not be related to you.