What is the modern scientific explanation for the two incidents mentioned, along with a comparison of modern medical opinion to what was stated therein?

The first incident describes the story of a woman who married while pregnant from her deceased husband. She thought her 'iddah (waiting period) had ended, but then gave birth to a full-term child four and a half months later. Imam Az-Zarqani explains this by stating that the fetus had become desiccated in her womb due to blood loss, and when her new husband had intercourse with her, the fetus became active and grew. Umar then attributed the child to the first husband based on his saying: "The child belongs to the bed."

As for the second incident, it revolves around a woman who bore a child after having relations with two men during the pre-Islamic era (Jahiliyyah). Umar ruled that the child should be attributed to both of them based on the statement of the Qā'if (one who traces lineage through physical resemblances) who indicated their shared paternity of the child, and he gave the boy the choice of being attributed to whichever of them he wished.

The fatwa indicates that these two incidents do not cause bewilderment. The first incident aligns with the fact that the minimum period of pregnancy is six months, based on the verses of the Qur'an, and it is not surprising for a woman to be unaware of her pregnancy. As for the second incident, it pertains to Umar's judgment based on 'Qafah' (lineage tracing) in the pre-Islamic era.