Children of the same father but different mothers are Half Brothers or Half Sisters, as are children of the same mother but different fathers. If two people who each have children from a previous marriage marry each other, then their existing children are step brothers or step sisters to each other.
That he does not know that he is their son is the reason why Oedipus kills his father and marries his mother in "Oedipus Rex" by Sophocles (495 B.C.E. - 405 B.C.E.).Specifically, Oedipus hears the prophecy that he will kill his father and marry his mother. He is correct in thinking that he is royal born and bred. But he is wrong in thinking that he is the son of Corinthian monarchs Polybus and Merope. This mistaken self-identity causes him not to restrain himself when he kills someone other than his presumed father and marry an older woman other than his presumed mother.
If the father and mother are deer, the mother would be called a doe and the offspring would be called fawns, but the answer might be different for species other than deer.
Your mother
Just call him by his regular name. It is know different from any other person. He just happened to be the kid of the mother/father your mother/father would be marrying.
Your half-sister's mother may be your mother, if you have different fathers. If you have different mothers and your father is married to your half-sister's mother, then you probably should call her "mother." If your half-sister's mother is not connected to your father (i.e. her father married your mother) then there is no relationship name for you to call her mother, other than "my half-sister's mother."
When your mother's mother and your father's mother are sisters, then your mother and father are first cousins to each other.
If you live in the United States, you simply say, "I am not going to marry her." You refuse to sign the marriage license. Other nations have different rules.
Courts in most States will usually lean towards keeping the mother and father of that child together whether one or the other is a minor. It will have to go through a court system.
Uh, they're your mother and father. Their relationship to each other does not change their relationship to you. Your parents are your parents regardless.
The genes in the tall mother and father do not necessarily match. One of the genes may be faulty, and might not be "compatible" with the other genes, making both go different.
Paternal is related to the father while maternal is related to the mother. Example: Your maternal parent is your mother and your paternal parent is your father.