So essentially, we have a protoplanetary disk filled with asteroids ranging from boulders to 30km long. Could they sustain a breathable atmosphere for humans, or would there have to be oxygen tanks and such needed. Additionally, could a ‘magic’ atmosphere generator help make the atmosphere breathable?
A protoplanetary disk is, in astronomical terms, a violent and deadly place. It is not somewhere you want to live. Gravity has spun all of this debris from the birth of the star into a disk. Everything that wasn't consumed by the star is now spinning around it.
Land to live is going to be an issue. You say there are asteroids of varying sizes. These asteroids are in an inherently chaotic system. Unlike 'normal' asteroids we have now, they're actively colliding because that's how we get planets (rocky ones at any rate).
This happens over millions of years, it is true, so in terms of a human lifespan it might be feasible and relatively safe, but the ultimate fate of that region of space is that there will be one thing there: a planet. Planets 'clear' their surrounding space of debris, since anything there gets sucked in and added to the planet. That's one of the reasons there are very few asteroids among the inner planets.
This can lead to incredibly violence. Earth was impacted by a planetoid the size of Mars billions of years ago, the debris from which formed the moon. The impact would have rendered both bodies practically liquid. This would be a somewhat regular occurrence.
Another word for a protoplanetary disk is accretion disk. This is what forms when material spins around a source, whether it be a star or a black hole. The issue is that spinning things make friction, which makes heat. Black hole accretion disks can be incredibly bright due to all the radiation they spit out (remember, heat is radiation too!).
This paper puts the average temperature of the Sun's accretion disk at roughly 230 degrees celsius for the first 5 million years. These things are hot compared to normal space stuff. This paper has some more information.
Now, onto atmosphere which is what you wanted. It is true that all elements came from the nebula, so all the elements needed for a breathable atmosphere are there too. Unfortunately, if we look at Earth, it's unlikely any of it would be breathable.
Most of the gasses in the accretion disk is just hydrogen. That's no good. The rest is probably like a gas giant; you'd find water, ammonia, methane.
Earth got it's atmosphere in a few ways. Volcanoes added nitrogen and carbon dioxide, as did asteroids slamming into earth. It did not have any oxygen. Any free oxygen was immediately taken into minerals, such as iron, to make iron oxide.
Oxygen didn't become a major part of Earth's atmosphere until the Great Oxidation Event, which is still the largest mass extinction event in the planet's history. This was done by bacteria who, like plants today, generated oxygen as part of their food cycle. It took a long time to raise oxygen levels and it required a lot of prep beforehand, like making sure that carbon dioxide was present beforehand. If that wasn't the case, life might have stayed anaerobic.
TLDR: if your humans want to breathe, they need to bring air themselves, if they can survive at all.
Normally, no. BUT. In The Integral Trees by Larry Niven, he proposes such a world, a gas torus around a neutron star and main sequence binary pair.