My mother was adopted and recently I was able to connect the dots and locate her birth families, so now the fun begins. I am confused in regards to the situation of a person having 3 paternal siblings (same father and different mother's) and a host of paternal 1st cousins. Since her siblings are considered 1/2 siblings does that mean that her first cousins are also considered 1/2 even though they would all share one set of the same grandparents?
Whether cousins are full or half isn't influenced by the relationship between your mother and her siblings, but by the generation above.
If the parent (father in this case) they share had full siblings, the children of those siblings are first cousins to your mother and her half siblings. They all share two grandparents out of four.
Cousins on your mother's mother's side, however, are unrelated to her paternal half siblings. They have no grandparents In common.
Half cousins are the children of half-siblings, e.g. yourself and any children your mother's half siblings have are half cousins. You share one grandparent with them.