A Sweet Theory.. but not mine.

[Christmas]

To say it was the remnants of Ulti´s castle is a lot more simple.
But your explanations can also apply.

To say it had nothing to do with Ulti's castle make it even more simple.

Maybe Gf´s and Weapons were created with time travelling properties.

Did you read my post or not? I explain how the GF came about. It is created out of other minds like how Greiver is created. As for the weapon,

The Garden of Eden story recounts how God created Adam and Eve, commanded them not to eat from the Tree of Knowledge of Good and Evil, and how they were expelled from the garden after they disobeyed Him, having been tempted by a serpent, and ate the fruit. As part of the Expulsion, cherubim and a flaming sword were stationed at the entrance to the garden, in order to prevent man from returning and eating from the Tree of Life.

A sword is stationed to guard Eden which you can draw it from Ultima Weapon in FF VIII. Lastly, this dude wield a sword.
In FF VI, Atma Weapon came with a package of a sword and a monster which is stated in the game itself stating.
In FFV II, Ultimate Weapon dropped a sword upon defeat. WEAPONS in FF VII are WEAPONS created by the planet. I dun think further details is needed since you played FF VII.
In FF VIII, Ultima Weapon wield a sword similar to Cloud's.

So there is no telling that Ultima Weapon is the sword itself since the sword is called Ultima Weapon too as based on the reference of Eden. As for Omega Weapon, I repeat myself:

So you're suggesting that the party may have dispersed Utima Weapon instead of slaying it, where it reformed into Omega during time compression. It's possible, and Omega does first appear as a nebulous cloud of evil that materializes after you ring the bells. Both seem to be able to change from a noncoporeal to coporeal state.

But it might be better to keep it to this: They are just optional bosses to give you a challenge and rewards and they most likely came from the moon since monsters came from the moon.

[Future Esthar]

Did you had evidence that the energy forms actually move on space?
Maybe only the bodies move.
Wasn´t Atma Weapon on Kefka tower also?

[Skyblade]

Did you had evidence that the energy forms actually move on space?

Do you have any evidence that they don't?

[Christmas]

Did you had evidence that the energy forms actually move on space?

I do know energy can be converted to other form of energy

Do you mean move on space as moving in space? What had space travelling gotto to with this?

And lastly dun forget this:

Do you have any evidence that they don't?

Maybe only the bodies move

What do you mean bodies move? If Squall defeated Ultima Weapon in the past, it won't have a body to start with.

Wasn´t Atma Weapon on Kefka tower also?

Didn't you read? I already explained:

Note that in FF VI, you fight Atma Weapon and Atma later in the game as an optional boss. Both Atma and Atma Weapon look the same and only with different paint job.

When you fight Atma, he mentioned something:

"Left here since birth....."

It is implied that it is left here in Kefka tower since it is born. And since Kefka Tower existed after the world is undone, so it imply that Atma didn't exist before Atma Weapon's time.

When you fight Atma Weapon he mentioned about:

"My name is Atma... I am pure energy, and as ancient as the cosmos"

Can energy be destroyed? Energy can be transfered and convert into other form of energy.

I reckon that the energy that made Atma weapon sorta converted into other form of energy which made Atma.

So the same might apply to Ultima Weapon and Omega Weapon in FF VIII since there is this incarnation of sword and monster going on and it started in FF VI itself.

And yes ATMA appear in Kefka tower and not ATMA WEAPON unless you are talking about the sword.