Can supplication change the destiny of a person for whom misery and Hellfire have been decreed, so that they become among the people of happiness and Paradise, or are these destinies unchangeable?

Whoever is destined to be wretched in the Preserved Tablet (Al-Lawh Al-Mahfuz) will remain wretched, and what Allah has decreed as an absolute judgment (qada'an mubraman) does not change. As for what is written by the angels, it may change with Allah's permission through supplication (du'a) and the like, and this supplication itself is part of the written destiny (qadar). This change and alteration occur in the branches and sub-branches, such as the daily and nightly deeds recorded by the angels. Allah establishes causes for their affirmation and causes for their erasure, and all of this does not contradict what He has known and written in the Preserved Tablet. Supplication affects what has been written, but this change was also written as a result of the supplication. What Allah has written for a servant is a matter of the unseen, which no one can know. The servant is obliged to strive in the means leading to salvation, for everyone is facilitated for what they were created.