The Predestination versus Free Will debate was one of the larger debates of the Classical Islamic era, and it has a lot to contribute to this question.
The monotheism of Islam can be said to be a reaction to certain forms of Christian Trinitarianism (among other things) and while it has a certain elegance about it, it does raise its own questions. It is plainly written in the Qur’an (the speech of God - another big subject) that there will be a day of judgment. People will be judged for their deeds, and according to their deeds they will be rewarded or punished. However, God is all-knowing and all-powerful. He knows - and is, indeed, present in - the past, present and future. Furthermore, God has the power to stop me from doing something. So if I do it, does that mean God allowed it? Am I the author of my own actions, or is God? If it is God, then how can he judge me? If it is me, then what can we say is not the result of God’s will?
Muslim scholars generally came to the conclusion that in order for God to judge, God must be just, in order for us to be judged, we must be free, and therefore, whatever evil is done by us is not God’s responsibility. However, this is not itself a good answer to the questions in the preceding paragraph. Ash’ari (a theological school of Sunni Islam) scholars argued that God creates all acts, both good and evil. We don’t create them. What we do is incline ourselves toward good or evil acts. And so they argued. A lot more development happened that I don’t want to go over, but basically, the general Sunni position settled around this idea that we have enough free will to be judged, but ultimately God has predestined everything, and we’ll just leave it at that.
So what does it mean to say that the position settled around something? Especially something so vague? How does a community defined in part by a theoretical (if not always in practice) lack of a religious hierarchy settle things? The answer lies in how creeds were approached in Islam. In the medieval Islamic world, creeds were almost always locally issued by private scholars and were documents that tried to focus on agreeing on what were the subjects of disagreement in the community. In other words, Islamic communities defined themselves through agreeing on what they were going to disagree about.
So an extremely basic position is outlined and debate (the Islamic word for theology, kalam, literally means discourse and refers to this debate) continues. Before the modern era, kalam was limited to scholars and was not for everyday people. On the subject of “do non-believers go to hell,” the Islamic community (to the extent that such a thing exists) agrees that there will be a judgment day. What happens to non-believers exactly is the ongoing debate.
Most scholars have not condemned 100% of non-Muslims to hell. This reflects the ambiguity in the Qur’an and Sunnah (Ways of the Prophet) on this matter that Butterflies mentioned. It also reflects different attitudes on the reasons different people have for not believing. Isolated island that has never heard of Islam? Guy living in NYC with Muslim friends but who has never read the Qur’an? Girl who was mistreated by Muslims? The non-Muslim scholar of Islam? All of these excuses are weighed differently. Trend-wise, the Maturidi theological school (Sunni, blended with Ash’ari over time, originally from Central Asia) claimed that God is evident and rationally discernible, so their views on the consequences of non-belief were harsher. The Ash’ari disagreed and were more lenient. Shia have their own range of thought.
All of that to say, there’s a lot of debate, like in Christianity. As for punishments, Muslims generally agree that hell is a place of fire and unimaginable punishments (though many try to imagine them). Good deeds can lessen your punishments, but at no point is it an enjoyable place to be. If anyone is curious, I can talk about whether hell is eternal or not in Islamic traditions (the short answer is, as usual, maybe), but I’m tired. Hope what I wrote makes some sense.