Islam believes in free will. Humans by definition are considered “free will” beings that can do good and evil and choose between them on their own.
“Predestination” is an English word. It implies that things are decided from “before” hand.
The concept in Islam is called Qadr, which is most popularly defined as “destiny.” It’s just faith in God. So has everything been “written?” The real question is, does it matter?
The Islamic (and Christian and Jewish) definition of God is an all-Powerful all-Knowing God. A God that knows everything and that includes the “future.” Humans naturally think of time as linear, which its not. For God, it can be more like a plane. So, in that frame of mind, God already knows what’s going to happen. But I don’t. Obviously, my actions and decisions will have a direct influence on my destiny. The fact that everything has been written doesn’t matter because we don’t know it.
The example: When I go to the movie theater, and I sit down, the movie starts. At this point, anything can happen. The characters make some decisions, their environment makes some changes, interactions, emotions, unexpected surprises, will all lead to a specific end, but really, it could be anything.
But wait–the movie’s end has been written. The film has already been written and shot and put into production, distributed, everything.
The characters in the movie always have control in the movie and free will, and I know that, and I don’t know how the movie will end. When I leave Interstellar saying like, “Yo dude, it was crazy how Matthew communicated with his daughter and they were in space and Anne was on that planet.” And I know it’s what Nolan planned all along. And that’s predestination. That’s destiny.