In feudal Japan, samurais could commit seppuku for various reasons : their lord died and they wanted to go with him, they dishonoured their title/family/lords... Like the tea ceremony, the making of a katana or the Bushido code, it was more and more codified through the years. What was the pinnacle of this codification ?
I heard, I don't know if it's true or not, that at some point after cutting their bellies, they had to write a haiku with their own blood and that the samurai responsible of the beheading should not completely cut the head but let it hang a little to the neck. Is all of this true, or is it just a rewriting of history like the romantic period rewrote "my ancestors the Gauls" in France ?
It is true that seppuku became more and more codified through the years, at least theoretically, but not necessarily in the direction of becoming more hardcore. Seppuku manuals of the Edo Period outlined a lot of ceremony and ritual, but often recommended seppuku without much or any disembowling. I recently wrote a reply on how seppuku was carried out and prescribed in the Edo Period in answer to this question: What would happen if a Samurai refused to commit Seppuku after losing their honor?. I think it would answer at least some of your questions.
Generally, yes, there's been a huge romanticization of seppuku that goes hand-in-hand with the popularization of "Bushido". It might surprise you to learn that Bushido in itself is a modern invented tradition, not a historical samurai code. We've discussed Bushido quite a bit on this sub before, so I'll refer you to my round-up of Bushido links and resources here.
We now primarily associate seppuku with losing one's honour, rather than the more historically common causes of seppuku: seppuku in war to avoid execution by one's captors, and particularly in the Edo Period, seppuku as the mandated form of execution for samurai. Seppuku preserved a man's honour, but he usually didn't undertake it because he decided he'd lost it.
The concept that samurai had to write a death poem in their own blood seems to be rooted in a few English-language books which are referring to one specific legend. In the 15th century chronicle, the Taiheiki, a warrior named Fuonji Shinnin is said to have committed seppuku along with his comrades in battle, and written out a death poem in blood on the pillar of the temple they retreated to. If anyone ever did manage this feat, it didn't catch on as a requirement or even a goal. Writing a death poem was an important part of a samurai's seppuku, and leaving it to chance and being able to function with your stomach cut open would be ridiculous. Death poems were written before the seppuku ceremony, sometimes long before. (On the subject of death poems, you may be interested in my April Fool's Day post READ THESE TOP SAMURAI DEATH POEMS AND TELL ME NUMBER FIVE DOESN'T BLOW YOUR MIND! The theme was historically-accurate clickbait.)
The popular idea that the second should leave some skin attaching the head seems to be rooted in Yamamoto Tsunetomo's Hagakure. So, for example, the Wikipedia article on Seppuku quotes Yamamoto as saying:
In the practice of past times, there were instances when the head flew off. It was said that it was best to cut leaving a little skin remaining so that it did not fly off in the direction of the verifying officials.
Yamamoto Tsunemoto, a samurai bureaucrat who longed for the "good old days" he'd never known, is a terrible source for how samurai thought and acted. But in this case, even this paragraph is taking him out of context. This quote is part of a section explaining why a second should aim to cut all the way through, even if they've heard stories of olden-time swordsmen who left the skin tag. Here's the entire section for context from Alan Bennett's translation of the Hagakure:
8-82. Leaving some skin when performing . When a certain man committed the second cut through his neck, but there was a strand of skin left so the head was not completely severed. The (observer) exclaimed, "There is a bit left!" This angered the man who dealt the mercy blow. He took the head in his hand and cut it completely from the neck. Holding it above eye-level, he bellowed: "Behold!" It was quite a disturbing scene.
There are stories in the past of heads flying through the air when the performed his task. For this reason, it was regarded better practice to leave a tag of skin on the throat to connect the head to the body, preventing it from rolling towards the officials. Now, it is considered better to make a clean swipe through.
A man who experienced cutting off 50 heads said: "Depending on the neck, it may offer as much resistance as if one were cutting through the breast ( ). You will not detect any resistance for the first three heads you sever, and the neck is easy to slice through. After cutting four or five necks, however, the resistance becomes quite pronounced. In any case, as it is a matter of immense importance, you will not mess it up if you cleave through the neck aiming to hit through to the ground each time."
Last but not least, you asked what the pinnacle form of seppuku would be. It depends on what you think seppuku should be, but I can share two eyewitness seppuku accounts from 1868 that are pinnacle-worthy in their own way. (Link is to my write-up on tumblr.) One is a refined, solemn ritual undertaken in a temple with great daimyo as witnesses. The other is a gory, violent bloodbath with defiant angry men and some very incompetent swordsman. Both of these seppuku incidents were undertaken to appease European diplomats, and both were highly effective orchestrated political theatre in their own very different way.