If they are not your daughter's children, then they are all step children. They will be called step-grand children. If they have children, those are step-great grand children.
If they are your daughter's children, you must know that they are your grand children as they are directly related to you.
Your step-son is the child of your spouse and another person, and is of no true genealogical relationship to you. So your step-son's children would also be of no true genealogical relationship to you either. However, they would commonly be called your step-grandchildren and you would be their step-grandfather or step-grandmother.
A bad relationship.
he didn't have any children
The sons and grandsons of a King or Queen are called are called Princes
Yes, he had two children called Henri and Leo
its called paternal care
You are your uncle's niece. You and your uncle's children are first cousins to each other.
The name of the relationship between your grandchildren and your sibling's grandchildren is called being "second cousins." The genetic relationship between two families becomes smaller and smaller through each generation, but no matter how weak that relationship is, it's still counted as a blood relationship. Your grandchildren and your sibling's grandchildren share a pair of great grandparents.
Abandonment.
It is no different than the relationship between straight parents and their children.
Yes, they had a great relationship.
Your children and your first cousin's children are second cousins.
Your children and your first cousin's children are second cousins.
Your cousin's children are your second cousins
A relationship is just that, like a friend and friend, or children with parents.
First Cousin, twice removed.
Your brother's children would be your nieces and nephews.