Is the half-sister entitled to inherit from her father, who bequeathed all his possessions to his wife (the questioner's mother) out of fear of the questioner's paternal uncles, and do the questioner's maternal uncles have a share in those possessions after her mother's death, knowing that the father does not know whether his daughter (the half-sister) is alive or not, according to the Hanafi school of thought?

Your father made a mistake by registering his property in your mother’s name, fearing for you from your paternal uncles. He could have gifted some of it to you or left it for inheritance. If the gift was merely a formal contract and your mother did not take possession of it, the properties become part of the estate and will include your paternal uncles and your half-sister in the inheritance. However, if the gift was real, your half-sister will not inherit, which is an injustice to her, and he should reconsider his action to ensure fairness. He is also obligated to search for his half-sister, provide for her, and take her into his custody. If your mother passes away, her husband (your father) receives one-fourth, you receive one-half, and the remainder goes to her siblings. If she passes away after her husband, you receive one-half and the remainder goes to her siblings.