The final battle

[Squall of SeeD]

But that´s the question.Ultimecia don´t live on the future but in the far past.Although Edea says the contrary you can´t prove that she is telling the thruth.Looking at it I would say that it was on the past and i will advance to say that it became the Garden Foundation.You have to quest everything on the game.Even if you believe that Edea is not possessed anymore how do you know that Ultimecia telled the thruth to Edea?.It can be a trap to deceive Seed.

How do we know she was telling the truth?:

1) Because the writer didn't say otherwise. The writer of a story is its God. Unless they put something there or imply its presence, it's not there.

2) It wasn't implied that Ultimecia told Edea she was from the future. The implication was that Edea gleaned it from her mind the same as she gleaned the hate in Ultimecia's heart from her:

Edea
"...I have been possessed all this time."
"I was at the mercy of Sorceress Ultimecia."
"Ultimecia is a sorceress from the future. A sorceress many generations
ahead of our time."
"Ultimecia's objective is to find Ellone."
"She is after Ellone's mysterious power."
"I know Ellone very well."
"Ultimecia is a very fearful sorceress. Her heart is filled with anger and
hate."

3) Deceive them how? That information was never used against them in any way despite them believing Ultimecia to be from the future from the moment she was first made note of.

4) Ellone sent Ultimecia's consciousness into the far past to cast Time Compression. The party then moved toward Ultimecia's time, which Ultimecia says was on the brink of Time Compression, meaning it hadn't fully passed over all time yet. The fact that she had to go to the far past to cast Time Compression suggests that the Time Compression wave would forward through time. Granted, we don't know the exact method of function for Time Compression, but there's no indication that Ultimecia isn't in the future.

5) Rinoa also gleaned the information that Ultimecia is from the future from Ultimecia's mind while being possessed:

Rinoa
"...I should tell you this before I go."
"I was possessed out in space. There was a sorceress inside me."
"Ultimecia, a sorceress from the future. She's trying to achieve time
compression."

There's never a single indication offered that Ultimecia isn't in the future while she's only ever referred to as being so. Unless you have some in-game support for this notion -- which you simply couldn't due to it never being presented by the game -- it's nothing more than an idea you fancy, and not even a theory in reality, as theories require some form of substantiation. Your canonical statement that Adel is Ultimecia is defeated by the canon of the game.

Besides, if Ultimecia were Adel in the past, that leaves the gaping question of "How was Adel alive in the present to rule Esthar, be confined by Laguna and the Adel Resistance, be sent into space, eventually be brought back down to the Planet, and then be killed by SeeD?"

Also, recall that the device Ultimecia used to possess Sorceresses from the past was called "Junction Machine Ellone." This was because it was created to simulate Ellone's power. Her power was the power to send the consciousness of someone she knows in the present into the mind of someone else she knew in the past:

Ellone
"...You want to save her. You don't want to lose Rinoa."
"Squall, I can't. I don't know Rinoa."
"I told you I can only send people I know in the present into people I knew in the past."

Also, seeing as how Junction Machine Ellone didn't exist in the past (or if it did, it didn't have the power it did during Ultimecia's time; in the game's present Odine states it was only a toy, implying it was something still in need of much refining), how would Adel have had access to it?