Does God already choose some people to go to hell?

No. In 1 Peter 1:1-3, you read there that we are chosen by God according to his foreknowledge.

Foreknowledge means he looks into the future. It's like if you see a home video made by somebody of people playing a game or something—passing a ball or hitting a ball in cricket or some game—you're not involved in it. You're watching it. You see somebody doing something. In the same way, God sees a video of the future.

We can only see a video of what is passed, but God can see a video of the future—what is happening a hundred years from now. Way back before he created Adam and Eve, he could see a video of the entire future of the entire history of humanity, 6,000 years. He could see everything, and that's called foreknowledge, seeing a video of the future. And, seeing a video of the future, he saw way down there in the twenty-first century somebody accepting Christ. "Chosen according to the foreknowledge" (1 Peter 1:1-2).

It's not that God picks names out of a hat or just arbitrarily chooses anybody. He'd be very unfair if he just chooses somebody and sends them to hell. God will never do that. Even an earthly judge would not be so unjust.