Your half uncle is the sibling of one of your parents, but not both. This means you share one biological parent with your half uncle.
Your mother's half-brother is your uncle, or half-uncle if you want to be exceedingly precise.
Many genealogy programs include a feature that calculates relationships between family members. The relationship between a grandmother's brother and a her grandchild is "grand uncle" or "great uncle." Learn more at 23andme.com.
your uncle is your sons great uncle
The English language recognizes no relationship between you and your husband's great uncle.
Your son would be the baby's uncle. Nobody would put such a fine point on the relationship to call your son the "Step-uncle" or "Half-uncle".
it great nephew :)
You are cousins
Uncle and niece.
she would be my cousin
Sexual
A half-niece and her uncle are expected to share about 12.5 of their DNA.
A person and their half-uncle are expected to share about 12.5 of their DNA.