Is the husband considered the guardian of his wife's daughter born of adultery when she is proposed to, and does the husband's care for his wife's daughter born of adultery qualify him to receive the reward of a father's care for his daughter on the Day of Resurrection?

The child of zina (fornication/adultery) is not attributed to the fornicator/adulterer. Therefore, the girl born from zina has no paternal relatives. Her guardian (wali) for marriage is the Muslim ruler, or the director of the Islamic center in non-Islamic countries. Some scholars are of the opinion that the mother's relatives, such as maternal uncles and grandfathers, take precedence over the ruler in guardianship. The stepfather is not her guardian for marriage. As for daughters interceding for their fathers on the Day of Judgment, this applies to children who died young. This girl is not the questioner's biological child, but he will be rewarded for raising her, spending on her, and taking care of her affairs.