An attempt at answering this:
Targoninas are just, or at least were just a normal race in the early time of current universe, like Runeterran people, from certain planet？ Or they are from another plane of existence or another dimension, whose existence form has always been spirit or some unknow cosmic energy?
I am guessing the latter. Scathlocke once implied they did not originate in Runeterra nor any other world but you can make the case that the celestial realm isn't a "world" proper (in the sense of a planet) so much as an entirely different plane of existence.
Aspects arise from Targonians (for example, some ascension form in the celestial world, same as Shuriman Ascension), or Aspects created Targonians? Or they are just two different type of creatures who work together?
Let's use two different terms for Aspects: mortal Aspects are the hosts, celestial Aspects are the celestials that empower them. The real Targon, the ones who enslaved ASol, are the celestial Aspects (and maybe, any lesser celestial entities that serve them). The people of Mount Targon aren't "Targorian" in the same sense as the celestial entities. They are just people, whose culture is shaped by the Aspects, living at what is effectively their doorstep potentially following lessons the celestial Aspects shared in times immemorial. They stand in Mount Targon and fight wanderers (celestial entities that enter Runeterra via the portal atop Mount Targon) and are sometimes chosen/empowered by the celestial Aspects as their agents (in which case, celestial and human merge, something similar, but not wholly identical, to Ascension).
So, what is this "inhabitants of the celestial real"? And why they care so much about the runeterra people?
Are they targonians？ Are they aspects? or they are someone else?
Unknown, maybe Targon is a specific group of celestials that did not give up on their little pet project. Maybe they have other motivations. This is just beyond what we presently know.
This means that the celestial beings is watching and guiding or even controlling the mundane people. Only for Runeterra? Or they just do this on all civilizations in this universe?
Runeterra seems to be a nexus of all the realms, it is the door and crossroads of all of creation (and beyond, even the Void has found a way in via Runeterra). Whatever celestials shaped Runeterra using the world runes seemed to have wanted to create a plane of existence that could outshine all others, perhaps they realized too late they had invited the Void to their realm. Perhaps Targon are those celestials that stand watch for the Void.
AND WHY THEY DO THIS? They are natural celestial beings? or they are targonians who arose by hand of aurelion sol from another ordinary planet, and now just wanna control all the universe?
We don't know, I assume they were curious and playing gods but, in their celestial purity, never quite understood free will. We've had info on Celestial Concepts, ideals manifest in the celestial realm, the very power behind mortal Aspects and Ascended. Perhaps they can only ever be what they are. Could War ever not be War and be something more or something else? Maybe they're slaves to their deterministic natures and never expected mortal life to not be constrained to a single idea like they are.
She mentions pantheon, leona and diana, and seems that she know them and know how the aspect ascension work.
If she is not an aspect,what is she? A targonian normal inhabitant???
Maybe but, again, we don't know. Maybe she was a celestial concept that abandoned her role to interact with the quirky physical reality.
Or just another race of celestial beings cause there are many races in the celestial realm like in Runeterra?
I do believe Targon is not the only celestial faction (Myisha wanted plausible deniability for trapping/killing celestials when she trapped the Darkin but the question is: who would hold her accountable? I'm guessing non-Targorian Concepts/Aspects).
They what is the relationship between Soraka and other targonians and aspects?
Not known yet.
So how many celestial races out there are in the universe?
They are all called targonians? Or just targonians conquered them all? so now it is a united empire?
I reckon that no, Targon is not the entirety of celestials nor do they control the whole of the celestial realm. I will leave this bit from Zoe's bio:
Following this unusual transcendence, Zoe journeyed to dimensions at the very edge of Targon's control, playing within realities beyond human comprehension.
So Targon is still expanding interdimensionally.
Why did targonians slave aurelion sol, if they are such a poweful race cause in Sol's lore it says targonians had already got the ability to colonize out of their home planet?
But why 3 years ago, a rioter said that what Sol's thinks and knows about Targonians is not 100% accurate because even he doesn't know what are targonians and where they are from?
A few things: bios are subjective. The most obvious examples are Jayce and Viktor. Bios reflect what the champion thought to a point. Aurelion thought they were a species that had expanded from their home world (in a way, he may be right). I believe he has since realized he was wrong and tricked. He likely saw what Targon wanted him to see at the time.
As for the reason they need him? Targon cannot operate in the material plane usually. Their mortal Aspects, the time space twisting around the Mountain and Soraka sacrificing her power to even come to Runeterra are examples of this. But Aurelion? He is a physical creature or, at least, more physical than them. He is the perfect weapon. They cannot exert their power in the material plane but ASol can.
Then, what are these celestial beings? Are they targonians ? aspects? or targonians and aspects?
If they are targonians with such power, then again, why they need to slave Sol?
We don't know. They may be completely unrelated to Targon or Targon as an empire may have been born from these would-be creator's actions (maybe the celestial Aspects were part of that group). The Sol question should be answered just before.
TL;DR: An attempt at synthesizing all this/my current thoughts:
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A group of celestials created Runeterra with some goal. Runeterra is the nexus of all known planes (physical, spiritual, celestial and the Void). Celestial Creators abandon the project.
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Targon, a group of celestial concepts (embodiments of abstract concepts) that would later be known as Aspects, is formed, relation with the Creators unknown.
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Celestial concepts cannot operate in the physical plane without significant cost so they rely on merging with humans who resonate with their essence and manipulate an arrogant star dragon into servitude (making him think they are a mere "physical" race). Now, they have the means to operate in the physical plane and use Aurelion to challenge any physical entities that could threaten their control. They begin to expand into multiple dimensions.
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Their foothold/gateway into Runeterra lies in a mountain known as Mount Targon. People gather there and build cultures around the Aspects, the Aspects likely manipulate them in small ways, ensuring they stand guard against celestial Wanderers that come from atop the mountain. The people of Mount Targon are not true Targorians and Targorians may not be an actual celestial race so much as simply the term for those few celestials that have active interest in Runeterra.
