In most families he would be called your nephew. But there is no real relationship. Unless your brother adopts him, which would legally make him your nephew.
the son would be the nephew
Step-brothers
If her son is from a previous relationship, then he would be your step-son.
Step Nephew
Great uncle / Great nephew
step brothers
step-granddaughter
No because that would be your cousin
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.
Your grandson is the great-nephew of your brother.
Step father and son
Yes, she did. She had the relationship of a mother that a mother has with her son. As most mothers do.