Is a specific act predetermined for a person, which they then perform by their own choice, or is a person able to change what has been predetermined for them?

What Allah the Almighty has decreed will inevitably come to pass. Part of it is beyond human will, for which one is not held accountable, and part of it is within one's choice. Allah has decreed, known, recorded, brought into existence, and willed the actions of His servants. Belief in divine decree (Qadar) is important, without delving into it excessively, which could lead to misguidance.