[q=Sir Bahamut]We also know it was activated in the far past where Ultimecia is sent.
The reason for this is never revealed.
[/q]It's explained clearly by either Edea or Odine, Edea I believe. In order for the spell to take effect, it has to be activated at two different points in time, a certain distance apart. So, she activates it in her own time, then uses her machine and Ellone's power to go back as far as possible and use the spell again. Imagine time as being like a pond. Drop a stone in one point, and you get ripples. Those ripples won't reach the other side, though; they'll just reach the side they're closest to. So, you drop another stone - i.e; cast another spell - at the other side, which represents the past for this purpose. The ripples now extend across both sides of the pond; the spells' influence goes far enough to set off the cascade that'll make time compress. When a building's being demolished, two explosives can do the job, but not if they're in adjacent rooms. They need to be far enough apart that the entire structure is affected. That's my interpretation of how time compression works, based on the brief expanation given in the game.[q=Sir Bahamut]Do you agree with me that all of time is compressed? It seems most logical. After all, we are told that "past, present anbd future will be compressed", and "past present and future" seem to refer to the general terms, no?
Nothing implies that it should only compress a small amount, so I think it is safe to assume it means ALL of time.[/q]As far as I'm concerned, it doesn't make a big difference. However, time and space are infinite; so to compress all time in all places would take infinite energy, which is not possible. Even if it's "done by magic". Magic is a manipulation of energy, so it couldn't have that kind of effect. Ultimecia's goal is to absorb the power from every sorceress who ever lived; that's her reason for compressing time. It's also explained if you cast Scan on Ultiimecia at a particular point during the final battle. Thus, she'd need only to compress time around her world, going back far enough to encompass the entirety of human history, thus ensnaring every sorceress.
You see, Squall and Co get to Ultimecias world by travelling THROUGH time compression. Once they're out of it, they are in Ultimecias world.
It is made clear that TC has not been completed.How does Squall and Co get to this place THROUGH TC when it lies OUTSIDE TC and TC hasn't been completed yet?
This is really a huge mystery.
Once again, a clear explanation can be found through a combination of in-game facts and logical conjecture. The team are able to travel to the future while time is compressing, yes. They do that through their own willpower, controlling their passage the way they would a magic spell. Time compression is a form of magic, so this is perfectly logical. It's also consistent with Laguna's instructions. By traversing the beginnings of the compression, they reached Ultimecia's time - where she unleashed the time compression spell. It's possible that the effects of time compression get stronger in the past, and take a while to "catch up" to the future; this'd explain why reality was severely distorted in their own time, but things are slightly less abnormal in Ultimecia's time (NB: The Ragnarok airship and the CC group both moved through time and space, to a different place in the world, during time compression. There's clearly a bit of disruption to Ultimecia's world). But then, during the final battle, time compression progresses. The process is nearing completion when Ultimecia's in her final form; reality has almost entirely dissipated. It is undone when she is defeated and her control over the process is disrupted. Time then de-compresses, and history is largely restored, except for Squall's panic and indecisiveness temporarily returning him to an earlier point in time.

The process of time compression is not a "huge mystery", nor is it "completely unexplainable". Of course, if you choose not to believe a particular explanation, that's up to you. However, you'll accomplish nothing by playing games and then saying, "Haha! This makes no sense at all! It's not spelled out in the course of the game, and if anyone has a theory, I can just say that their theory's not in the game either! This proves that the game is stupid and makes no sense!"
Such thinking is pointless. A good story doesn't assume that the audience is stupid, that they need every detail spelled out monosyllabically. Conjecture, theory and personal opinion can add colour and detail, just like the R=U theory.