Do half-siblings from the father inherit a house that the father registered in the mother's name before his death, after the mother's death?

If the father gifted the house to the mother and she took possession of it during his lifetime, then the house belongs to the mother, and your half-siblings do not inherit from it. However, if the mother did not take possession of it during the father's lifetime, then the gift is invalid, and the house becomes an inheritance for the heirs. And if the father intended by withholding the house from your half-siblings to deprive them, then the gift is invalid, and all children inherit the house.