Is a wife who dies two hours after childbirth considered a martyr? What is the duty towards the daughter? And is the husband considered a guardian of an orphan?

If a woman dies with a fetus in her womb, or dies during childbirth, or thereafter during the postnatal period (nifas), she is considered a martyr, Allah willing. This is based on Prophetic hadiths that mention the martyrs of the Ummah and state that "the woman in postpartum bleeding (nifas) will be drawn to Paradise by her child through its umbilical cord" and "a woman who dies with a child in her womb (bi-jumuʿ) is a martyr."

As for your care for your daughter after her mother's death, it involves attending to all her needs, including her expenses, clothing, upbringing, and discipline. This is a duty upon you, and you will be rewarded for it if your intention is sincere for the sake of Allah. In this case, you are not considered a guarantor (kafil) of an orphan, because legally, an orphan (yatim) is one whose father has died while they are young. The hadith that mentions the sponsorship of an orphan by saying "his or for another" means that the sponsor could be a relative of the orphan ("his") or a stranger ("for another"). Your duty towards your daughter includes providing for her, and focusing on her upbringing, teaching her matters of her religion, and instilling Islamic creed in her.