lack of oxygen near the south summit
That part wasn't explained in detail in the movie (probably due to lack of time; the movie was already 2+ hours). In reality, there was no lack of oxygen bottles at the South Summit. There were several full bottles. What happened is that Andy Harris, probably in a hypoxic state, was telling everyone that the oxygen bottles were empty, which created confusion. Jon Krakauer and others, while descending tried to convince him that the oxygen bottles were full, but he wouldn't believe it. Since the only way to tell if the bottles are full or not is to attach them to the regulator on the mask, it is thought that Andy's regulator was frozen up (or malfunctioning), which caused him to think that the bottles were empty. In his oxygen starved and hypoxic state, he wouldn't believe it when others told him that the bottles were full. Apparently Andy eventually figured it out and carried some full bottles up to Rob Hall, but no one ever heard from him again and no one know's what happened to him after that. The movie portrayed the events briefly, but it didn't explain what was going on in detail.
Also, I was confused by the mention of David Breashears in the movie. Was he on one of the guides or clients?
As mentioned above, he was making an IMAX film with Ed Viesturs and others. They decided not to do a summit attempt at the time of the accident since they felt that there were too many people on the mountain, which would interfere with the filming. They decided to hold off the summit attempt until the crowds thinned off. David Breashears played an important part in the even since they had oxygen and other supplies cached at the South Col and at other camps. When the tragedy happened, the IMAX team/Breashears let (what was left of) Hall's and Fischer's expeditions have access to their cached oxygen and supplies (on a different note, after the tragedy, many expeditions packed up and went home, so the IMAX team was able to replace many of the items that they had generously let others use).