Seals

One..
Amano - 1
Touya - 2
Hazuki - 3
Shana - 4
Ruou - 5
We're missing 1
But that doesn't make sense in the first place cause Shana and Ruou never died.
A group of Shinma worriors came to earth, fought to close Hell's gate. Only Raki, Garai and Touya left. Garai killed Raki. Made six souls including Touya's and his own to build a barrier. If Ruou's and Shana's souks were used as part of barrier, they should've died and reincarnated just like the other three.

No, there were ten seals, but 13 warriors with divine beasts. I think that Raki, Garai and Touya were with six other warriors at the gate, but they died and their souls were used to finish sealing the gate ...

I mean 5 plus Garai - not six

yeah but Ruou and Shana were not part of the 8 who came to earth. That's why they can't make the situation head or tail. Ten seals were what Amano saw in his mind. Prince's Ren's barrier only has 6 seals. If you take it as 5 warriors plus Garai, then what happened to Touya? I'm pretty sure Touya seal was used in barrier cause the Himi clan descendants saw the seal. If we calculate all five warriors and Touya, Garai can't be part of the barrier cause his soul is already overwhelmed by keeping the forbidden spell in place. Or if we consider Garai as part of the barrier, one unnamed warrior escaped the forbidden spell so his soul should have been transferred back to their realm, not being chained down on earth by the spell.

I think the six seals were the five warriors and Garai, the ten seals include Raki and Touya - I don;t think Touya died at the gate, Garai was trapped body and soul and Raki was only trapped physically (so his spirit travels to Kou) Touya - don't know what happened but his spirit travelled. Garai's did not - which is why Kouichi has an incomplete binding? Just speculating of course. I am not sure why there were only 10 seals for 13 warriors though, that answer may yet come.

I'm also inclined to believe that Touya was not part of the barrier because that would explain why 5 warriors' souls were not reincarnated. Garai's soul was damaged beyond repair so Hazuki only inherited Tarupa without Garai's mana. Garai's soul cannot possibly be reincarnated. Raki's soul reincarnated cause Garai saved his soul with forbidden spell. Touya's soul got reincarnated cause he was not part of the spell. He only used his body to seal Raki's soul inside it so the damaged soul can heal over time.
But it's confusing because Himi clan actually knows the Touya seal. Himi doesn't have the knowledge of the other realm. They can only see what's in front of them. They only know the six seals which they found on prince Ren's barrier. So why are the Touyas part of the clans to protect the barrier?

Well, they were the traditional clan that provided the 'strongest warriors' to the Shinma and seemed to adopt the role of protector, so perhaps that tradition was passed down?

I think you're talking about the real Touya clan from the other realm? The Touya clan Himi knows is called that way only for namesake. They don't even carry the same Kanji characters. The real Touya clan's name is written with 'blade' and 'evil'. Anyway, I don't suppose Garai and Touya left any offspring. I wonder where all these clans popped up from. But I guess Garai was the one who gave the name to fake Touya clan. Although, he couldn't pass down the same mana because it wasn't his own mana. So the name became in different meaning. It still doesn't explain why Himi will see the Touya's symbol on the barrier. According head lady of Himi, there are only six seals. Then Touya's seal shouldn't be part of the calculation.

The Tohya mana was not passed down genetically, at least I don't think so, it was given to whomever was the strongest and could win the blade at the temple. As for the Touya clan, I am thinking that if they come from parallel universes, then sometimes similar ancestors could appear? I know the Shinma had the 'elf' ears that the people in this world don't, but that could be throwback genetic mutations. Hopefully these things will be explained in future chapters.