What is Time Compression?

[Sephiroth]

Ultimecia should only exist in 2 time periods, when Ellone send Ultimecia into the past, she should no longer exist in Squall's time Ultimecia in Adel's body in the past and Her future self.

No, she should exist in more than two time periods because of the presence of one consciousness in more than 2 time periods and I have explained, how. And even in Squall's present her consciousness is still present at the end which is needed for her plan. Her consciousness in her own body, her consciousness in Edea/later Rinoa and then because of Ellone's ability the consciousness in even more time periods. You think her abilities are that limited. But they are not. She can somehow connect her consciousness with a time period where the powers of an already dead Ultimecia existence was given to another woman and control many more witches in the past, so many Edeas/Rinoas when they got the power of another dying Ultimecia. And like I said, there is still Ellone's ability. Ultimecia combines those powers to transfer her consciousness and cause the paradox of them being past, present and future at the same time (short: she just uses manipulative powers to control time). Whether this makes too much sense or not is not relevant. It does in Final Fantasy VIII's universe since Ultimecia wants to use many abilities to control time completely. And that is all which is important about it.

But She said she wanted to make Squall and others her slaves for eternity.
Which means there's no way she is the only who can exists.

It is. The entities are connected to her alone since she is the only one who can resist the destruction via time compression. She is the one who does not erase the existence "Ultimecia" because she is immune to it.

Nobody really understood what Time Compression is.

I cannot speak for you, however I do know and do understand what the Time Compression is.

You think Time Compression would allow people to do this and that. But that is not true. That is just the beginning of the Time Compression which "opens the time windows" when the time periods are connected, so the border between them begin to vanish and they are slowly becoming one. And so they can travel throug time. Later it would not be possible anymore since there a) are no time periods to travel and b) is no being left to travel. When the Time Compression is complete, there is nothing left but Ultimecia herself. Does she have anything from that? That is not the best question for a Final Fantasy villain. Sometimes the destruction of existence itself is the only thing they want. And the desire to reach this goal is the only thing we really cannot understand, even with all the given "reasons" since we are not like those superhuman beings who manipulate not just physics but meta-physics themself.

I have the Final Fantasy VIII Ultimania which explains the whole Time Compression plot and Ultimecia's abilities, including Griever's origin a lot better. I could continue and explain all of it, but believe me, it is a bit more complex than that and the easy way I explained it is enough.

I hope you understand it a bit more now. It is a weird topic, yes. But only because the topic time, time travelling and all is something no human being really understands so for such stories you can create many things and write it the way you want. Especially if you use a villain who can control time this way anyway.

EDIT: Your doubts don't change anything. I know it. Square Enix writes things, I read them, I know them. Just because you don't know or understand something it is not something which cannot be understood. I am sorry.

"Anyone claiming that they know it's possible is being bold, let alone saying they understand it."

It has nothing to do with being bold but with playing the game, reading the Ultimania and concluding. So don't say anything against others just because you did not. "Don't try to understand it in any real world concept" is a totally unnecessary sentence because those who understand it already combine it with the world of Final Fantasy VIII and Final Fantasy VIII does in fact have law, physics, et cetera which can be used and should be used to understand it. Time Compression can be understood in general. Nobody says that it is explained to the very last word but as far as possible it can be understood and saying "it cannot be understood" and "no one understands it" is wrong.

"Think about it properly for just a second - wouldn't compressing all moments in time together just be one great big paradox?"

No it wouldn't. That is not what Time Compression is like and shows that you really do not understand it. Calling other people "bold" is a bold post of yourself.

EDIT II: That is not what I said. I wrote you a PM.