1. How did you know theres no recorded about the otsutsiki clan? What if in the uchiha tablet the reason why black zetsu changed it it's because it was originally written about their existence? What makes you think theres no proof about their existence?
There are several things that allude to there being no recorded history of the Otsutsuki family. One such example is Hagoromo himself. It wasn't common knowledge that the legendary Sage of the Six Paths had children and those that did knew did so through having read the Uchiha Tablet. It was also entirely unknown that he had a brother in Hamura, or that there was an entire clan of them on the moon.
No one aside from Madara had heard about Kaguya either, who was a very prominent figure in society at one point, acting as the ruler. Yet the only recorded history of this was through the Uchiha Tablet. Then we have the dialogue between Naruto and Sasuke as they grow older. Sasuke constantly looking for information regarding Kaguya and her clan as while they now know about them, they know extremely little about them.
2. Infinite tsukoyomi was written in the uchiha tablet, the only way to find peace, madara didnt knew about the side effects because he been brainwashed by the black zetsu like I said black zetsu changed what ever written on the uchiha tablet.
Then exactly how would Itachi know about the side-effects? The ritual required to cast the Infinite Tsukuyomi was only written on the Uchiha Tablet, but was originally written as a warning by Hagoromo that was later changed by Black Zetsu. Hagoromo states himself that he left only that tablet behind in hopes that it would act as a warning. There was no other records of the Genjutsu and thus the only place Itachi could've learned it from was the tablet. Obito also seemed to lack some knowledge regarding this plan, believing that one needed the Shinju to cast the Genjutsu and not the Rinne-Sharingan.
The only one who knew the entire plan was Madara and even then he didn't know the entire effect of the plan as Black Zetsu was manipulating him. At best Itachi would believe the same Madara did, but there is no implications that he did. In-fact, Itachi didn't know who Tobi was, only that he likely wasn't Madara or that he was severely weakened Madara. He didn't know that Madara had obtained the Rinnegan and passed it on before dying. Nor did Itachi know about the Gedo Statue's origin or location.
3. Pain's Rinnegan is the living proof that the otsutsiki exist, if theres someone who will itachi to the otsutsiki clan it's the one who got the rinnegan. Makes sense right? So far that's probably the only thing that leads him to them.
Nagato knew nothing about the endgame plan or the origin of the Rinnegan. Nagato believed himself to be the "reincarnation of the Sage of the Six Paths" simply because he had the Rinnegan. A Rinnegan that wasn't even his own, and was borrowed from Madara. He didn't know Hagoromo's true name, as it wasn't recorded anywhere other than the Uchiha Tablet as far as we know. (Even then it wasn't outright stated that Hagoromo's name was recorded there either). The warning on the Uchiha Tablet also required the Rinnegan to fully read.
Meaning Itachi wouldn't be able to read the entire thing that explained Kaguya and the Genjutsu as a whole. Hence the only way for someone to know would be for Madara to tell them. Madara and Itachi never interacted, not for one second.
4. What the fck they didnt existed? What are you saying? You suck fool, they existed, it's even said by the white zetsu that itachi extracted the items to his susanoo, they exist but someone itachi found a way to put it in his susano.
No. That is where you are wrong. We know that Orochimaru knew the blade existed, though not much more. Black Zetsu also mentioned that Orochimaru had been searching for the blade, but as he also explains, it isn't a weapon or item you can find as it is a spirit item. This is what Black Zetsu has to say about the matter:
Black Zetsu Chapter 392 said:
No wonder no one's been able to locate it... It's a spirit blade that has no physical form... The Totsuka Blade, also known as The Sakegari Blade, is a sword of sealing. Orochimaru had been looking for this sword for a very long time.
This quote is from a being that as been around for thousands of years so we can take what he states as pretty good evidence, especially in instances like this where he is just thinking it to himself and not trying to manipulate anyone. We learn a few things about the weapon. For one we know that the weapon is a "Spirit Item" and as such has no physical shape. It cannot be "found" in the world and cannot be "picked" up like a normal sword. This is something that Black Zetsu didn't seem to know himself as he was shocked to find out.
We also learn that despite the weapon not being a physical item you can find and collect, there is legends about it. Meaning it (or something akin to it) has existed at some point in history. What we don't know is if Itachi actually has the famous blade or if he simply has a blade that has the same traits. If he has the famous blade then it wasn't something he found, but something that is tied to his spiritual power.