Is one rewarded for doing a deed without knowing its merit, such as saying "Subhan Allah wa bihamdihi, Subhan Allah al-Azim" (Glory be to Allah and with His praise, Glory be to Allah the Almighty) without knowing its merit?

It is not a condition for earning the reward of an action to know its virtue or the measure of its recompense. Rather, the condition is to perform it in the correct, Islamically prescribed manner, based on the Almighty's saying: "So whoever hopes for the meeting with his Lord, let him do righteous work and not associate anyone with the worship of his Lord," and His saying: "But whoever desires the Hereafter and exerts the effort due to it while he is a believer - then those are the ones whose effort is appreciated." And based on the Prophet's (peace be upon him) saying: "Deeds are but by intentions, and every person shall have but what he intended," and his saying concerning Tasbih (glorification): "Whoever says 'Subhanallahi wa bihamdihi' (Glorified is Allah and praised be He) one hundred times in a day, his sins will be forgiven, even if they were like the foam of the sea." Knowing the virtue of an action or its reward is better, because it leads the one who knows to ponder the meaning, to have presence of heart, and to endure hardship; hoping for the attainment of reward and recompense, just as the Prophet (peace be upon him) said concerning the virtue of Fajr and Isha prayers in congregation: "If they knew what was in them, they would come to them even if they had to crawl."