Why was the word "brother" used in the verses of inheritance with a general connotation, and how is a distinction made between a full brother and a half-brother in inheritance, especially since full brothers inherit from a full brother or full sister, while a half-brother does not inherit, and similarly in the mother's inheritance?

The paternal brother inherits from his deceased brother, unless there is someone closer to the deceased than him, such as his son or father, or someone with a stronger kinship tie to the deceased, like a full brother. The full brother is prioritized because he is related to the deceased through two sides (the mother and the father), whereas the paternal brother is related through one side (the father); based on the hadith (definition): "Then to the nearest male." Thus, the stronger in kinship excludes the weaker.