***SPOILERS AHEAD***
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Here is a start of my theory. There are just little tidbits, not a full-out theory, though.

I can see how Aeris could be the descendent of Tidus and Yuna. Since she is related to the ancients it definitely ties back to the mythical nature of Tidus and Yuna. Yuna being a Summoner gifted with magic and Tidus being a dream of the Faith, coming from the legendary Dream Zanarkand. Good stuff for an Ancient-type race.

Other possible character connections that could be great nostalgia: What about Tifa being the ancestor of Wakka and Lulu? Hey, how else could you explain... the chest? =)

Another fun possibility is having Cid of FF7 be an ancestor of Rikku and Gippal, or any other member of the FFX Cid family tree. Having Al Bhed blood would be a great way to explain Cid's gift for technology, and also the FFX Cid connection can explain Cid's know-how when it comes to building a space ship.

Now to theorize about the world, here are some tidbits...

The FF7 airship has some similarities to the design of the 1st airship in FFX. The downsized nature of it can also be explained by stating it is a product of actual built technology by the Shinra corp. and not just an excavated ship from Spira's past.

Explaining the technology... Since the Spira of FFX/2 is just now starting to embrace Machines (They even begin calling it machine instead of machina) they are only now learning more about it. The Al Bhed have been digging up old tech for years and it is a matter of time before they build their own technology from scratch.

Since the power source of the old Spira isn't known, Shinra comes into play. Just like any other powerful man in history, Shinra has the right friends and right resources to become very influential. His harnessing of the energy in the Farplane thus creates the theory of Mako energy, and through the generations his ancestors come up with many new inventions and figure out better ways of using this energy.

Materia is also an invention of the first Shinra. He expands on the dressphere idea and adds Mako to create Materia. Tidus and Yuna are even first to try it out!

After awhile when Mako becomes prominent, Midgar is constructed on top of the ruins of Zanarkand. Also, the new Spiran technology is everywhere.

After some time Spira discovers that the planet is deteriorating because of the Mako energy. They find out that it is the planet's lifestream. The Shinra corp., however, generations removed from its founder, refuses to give up mako. A war ensues between Spira and Shinra. This directly parallels the war between Zanarkand and Bevelle of Spira's past, as Bevelle fights Shinra and Midgar, which was built ontop of the ruins of Zanarkand. Ironically, the older was was between Bevelle, which was technologically advanced, and Zanarkand, which was more advanced in the arts of Summoning. Now however, the new Zanarkand called Midgar is advanced and Bevelle is less advanced. However, Spira eventually wins and the leaders of Shinra go into hiding. The Spirans begin to stop the use of Mako and once again stop using technology and Midgar is abandoned. Bevelle once again becomes the center of life in Spira.

Now the more wide open area is how Spira becomes the FF7 planet. There has to be some kind of disaster. This disaster happened 2000 years before FF7. This was when Meteor crashed to the planet. This happened because Shinra was once again on the uprise, having been hiding for many years, and began to start another war for power. To combat this, the Spirans summon meteor as their last hope. On it, however, was a new Sin, named Jenova, which began spreading its virus. The Spirans (Or Cetra in FF7) began turning into fiends, and thus, the race was losing alot of its history and knowledge of Spira. After Shinra and the Cetra teamup and begin containing Jenova the world is completely different as a result from the metoer. This explains the geography of the planet in FF7. Also of note, Bevelle was completely destroyed by the meteor.

Thus, Midgar is once again re-constructed, the Cetra begin dying off, and Mako energy is once again coming back. Jenova is forgotton, and the world of FF7 is now in full cycle.

Oh, another aspect of FF7 that can be explained is that of the Promised Land. Notice any similarities to the Far Plane of FFX? Definitely something to touch on.