The Red Star was a blazing star in the heavens above Mata Nui. Of all the celestial bodies, the Red Star most governed the interpretation of prophecies about the island and its inhabitants.
The Red Star was quite a bit smaller than Mata Nui.
While orbiting Aqua Magna, the Red Star could be seen dimly from Bara Magna. The average inhabitant of Bara Magna knew absolutely nothing about the Red Star. One needed a telescope to view the Red Star from Bara Magna; no one on Bara Magna had a telescope.
The Red Star had a proper name.
Neither Mata Nui nor Teridax ever needed to know what was inside the Red Star. No Great Being was ever inside the Red Star.
Mata Nui was supposed to be a self-sustaining system, and certain individuals played very important roles in maintaining it. In addition, it necessarily had finite resources for producing new beings to replace any lost in accidents or other circumstances. The red star was designed to address this problem. A being who died inside Mata Nui would be teleported to the red star, where its essence would be transplanted into another body, and it would be sent back. Unfortunately, as with so many things related to Mata Nui's construction, it did not work very well. Teleportation to the red star worked, but teleporting back did not. As a result, a lot of newly revived dead beings were stuck on the satellite with no way to get back home.
When a being died, its body was teleported up to the red star. For this reason, there were no graveyards in the Matoran universe. Then, either the body was repaired, or a new one was made to house the being's consciousness. However, if a being's body was utterly destroyed, the red star had nothing to work with, and the being would not be revived.
The lightning from the red star that transformed the Toa Inika served as a fail-safe to create new Toa outside the Mata Nui robot in case they were ever needed. After all, there were never supposed to be Matoran outside the robot. The Toa Mata failed to wake Mata Nui on time, and thus there were still Matoran outside on the islands of Mata Nui and Voya Nui.
Fulfilling one's destiny did not preclude someone from being revived. The red star was meant to address the fact that not even Mata Nui could be self-sustaining if he lost too many beings (e.g. to an accident). In the same way, a person could not survive if he lost too many blood cells without replacing them.
Rahi could be revived, since they played a role in Mata Nui's functioning as well.
Unlike the Kanohi Tryna, which brought a being back right away with all the damage, the red star took a good deal longer but repaired the damage.
The red star did not discriminate when it came to which beings it revived. It worked for all dead beings with an intact body, as everyone had some role to play in the universe.
Anyone who died and whose body was not disintegrated was revived on the red star. This meant that Matoro and the members of the Brotherhood of Makuta were not revived there, as they had no bodies left. As long as there was a body left to work with, no injury, like a missing limb, would prevent a being from being revived by the Red Star.
The Red Star stopped working quite a while before the events of Mystery of Metru Nui, which is why no one was looking around for Lhikan to come back.
As of the end of the story, the Red Star could not teleport beings to it, since the system was broken [sic?].
Someone who was revived on the Red Star and had teleportation powers could arguably have escaped from the Red Star back to the Matoran Universe.
Beings revived on the Red Star had a tendency to be so confused by the experience of dying and coming back to life that they did not know where they were. The beings that Pohatu and Kopaka encountered, for example, did not seem very coherent.
The red star on the map that Tarduk found marked the location of a Great Being facility, the one in which the Red Star was built.
A completely organic being like Tren Krom could not be revived by the Red Star.
It is not necessarily true that the Red Star could not revive beings who were outside of the Matoran universe; in fact, being inside or outside of it may not have made a difference. It was keyed in to inhabitants of the Matoran universe.
Beings who required Kanohi, such as Matoran and Turaga, were given masks in the red star after their bodies were teleported there.
Beings who were revived in the red star were supposed to be able to remember everything from their past life, at least eventually. However, the process of being brought back to life tended to be very traumatic, so it took a while for one's thoughts to be unscrambled.
Beings who were revived in the Red Star were given a replica of the body they were in at the time of death. For example, a Turaga would not be put in a Toa's body.
At the end of the story, it was unlikely that the Red Star would continue to transform Matoran into new Toa on Spherus Magna.
If someone died on the Red Star, he would not be revived. The system was pre-programmed to bring bodies up from the Matoran universe and return them there. The Kestora did not do this programming and probably did not know how to alter it, since there was no real reason for them to have that knowledge.