Is it a prerequisite to intend to count all the benefits and rewards associated with a righteous deed—such as the Duha prayer—in order to obtain them, or are these benefits acquired merely by performing the righteous deed, even if all those benefits were not intended?

The intention required by Islamic law is for a servant to perform acts of obedience seeking the countenance of Allah the Almighty and drawing closer to Him. If he does so, he will receive the reward associated with the act of worship, whether he knows it or not, and whether he intended it or not. Thus, intention in Islamic law is the will and inclination towards an action, seeking the countenance of Allah and complying with His command. The hadiths that mention the rewards for deeds are meant to encourage people to do good, and it does not mean that the reward is only attained by remembering and intending it. Allah's grace is vast, and the reward is attained even by those who are unaware of it, such as the one who gave water to a dog and was forgiven, or the one who utters a word of Allah's pleasure, not thinking it would reach what it did, and Allah writes His pleasure for him because of it.