The common ancestor is your parents.
Your children and your sister's children are first cousins.
Your grandchildren and your sister's grandchildren are second cousins.
Your great-grandchildren and your sister's great-grandchildren are third cousins.
Yes, he is their great uncle.
No, they`d be the second sisters great nieces and nephews
They are your great nephews and/or great nieces. Alternately, some people say grand-nephews, grand-nieces.
Real sister, half sister, or step sister
sister in law.
Your sister's sister is your sister.
Your son's children are your grandchildren.
You would be their great Aunt.
Your sister's children's children are her grandchildren.Your children and your sister's grand children are first cousins, once removed.Your grandchildren and your sister's grandchildren are second cousins.
Great aunt
No relation whatsoever. You will be an aunt or uncle to your sister's child and your brother-in-law's sister will be the child's aunt, but that's as close as it gets.
Your mothers sister is your Aunt