Your parent's first cousin's children are your second cousins.
Your children and your second cousin's children are third cousins.
Your children and your second cousin - or likewise you and the children of your second cousin - are second cousins, once removed.
You and your parent's first cousin are first cousins, once removed.
If two people are first cousins, their children are second cousins. If two people are fifth cousins, their children are sixth cousins.
If two people are first cousins, the children of one are second cousins to the children of the other.
First cousins born on the same day are called "double first cousins." This term is used when two siblings from one family have children with two siblings from another family, resulting in their children sharing both sets of grandparents. Double first cousins share a higher percentage of genetic material than typical first cousins.
Two people who have at least one grandparent in common are first cousins. Your son and your stepbrother's son may be first cousins, or may be unrelated. Even if they are unrelated that can call each other first cousins if they get on well together and want to do that.
The children of first cousins are second cousins to each other. Where two people are first cousins to each other (call them Joe and Ed) Joe's children and Ed are first cousins, once removed, and Ed's children and Joe are first cousins, once removed. Joe and Ed are in the same generation. Their children are in the next generation. "Once removed" refers to people who are in different generations and there is only one generation difference between them, as is the case with parent and child. Grand parent and grandchild, for example are two generations removed from each other.
If you are referring to YOUR grandmother and grandfather then your children are their great grandchildren. If you are referring to your parents, then your children are their grandchildren. The primary kinship dominates.
The children of your grandmother's brother (of your great uncle) are your parents first cousins and your first cousins, once removed. The grandchildren of your great uncle are your second cousins.
Two people whose great grandparents were siblings are third cousins to each other. The children of siblings are first cousins. The grandchildren of siblings are second cousins to each other. The great grand children of siblings are third cousins to each other.
The first cousin of your dad's first cousin is also your your dad's first cousin or is not related to him or to you. The children of two first cousins are second cousins to each other. So the son of the first cousin of your dad's first cousin is either your second cousin, or is not related to you at all.
Children of sisters are first cousins. Grandchildren of sisters are second cousins. Great grandshildren of sisters are third cousins.
Your first cousin's child is your first cousin once removed. Once removed means one generation apart. Your cousin's grandchild would be your first cousin twice removed--two generations.
There's every likelihood that the children of first cousins will be "normal" but there is a somewhat increased risk that the children of two such close family members might have a genetic disease or birth defect. The increase in that risk is not huge unless the two first cousins are at the end of a long line of first and second cousin marriages.