There are Aunts, great aunts, great-great aunts, et al.
A second aunt would be if you have two aunts and you prefer one over the other. But no there isn't.
no
Your great aunt's grandson is your second cousin.
You are the nephew if you are male and a niece if you are female.
If your greatgrandmother is his great aunt then you and he are second cousins, once removed to each other. Your parent is his second cousin.
The grandchild of your great aunt is your second cousin.
Your parent's aunt is your great aunt. Your great aunt's daughter's child is her grand child. You and your great aunt's grandchild are second cousins.
Your grandfather's sister is your great aunt. The grandchildren of your great aunt are your second cousins. Their children, the great grandchildren of your great aunt, are your second cousins, once removed.
You and your great aunt's grandson are second cousins. Your great aunt was the sibling of one of your grand parents, so your parent and your great aunt's child were first cousins. You and the grandson are members of the next generation and therefore second cousins.
Your grandfather's sister is your great aunt. The grandchildren of your great aunt are your second cousins. Their children, the great grandchildren of your great aunt, are your second cousins, once removed.
Your aunt's children are your first cousins and theirchildren are your first cousins, once removed.Your children and the children of your first cousins are second cousins to each other.
If your great grandmother was his great aunt you and he are second cousins, once removed.
Your great aunt's daughter's children (her grandchildren) are your second cousins.
If your grandmother was his great aunt then you share a great grandparent and are second cousins.