First of all, if you want a entire explanation to the powers of the two clans, please see this thread:
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Now unto answering your questions. ( Though they are already answered in that thread. )
Sorry, I don't think your thread is a canon fact. Besides, from our current discussion, it is clear that you are much influenced by your own opinion.
Hagoromo didn't have the Sharingan as the Sharingan is a devolution of the Rinnegan which was most likely created by combining the Ōtsutsuki lineage and the power of the Juubi.
Again, not only these are your own interpretation, but you are also wrong and ignoring the canon. First, Sharingan is not, and has never been a devolution of the Rinnegan. If we consider the initial elder son's eye, it was not a sharingan, but a spiral shaped eye pattern.
This is is another evidence that Rinnegan is not just a power confined in the eyes. In order to get the Rinnegan, you need both the body and the eye of Rikudo.
Thus, the proper way of speaking of Sharingan is that it is a devolution of the elder son's eyes, which are spiral. This is a manga fact.
No matter how an Uchiha evolve, he will never have Rinnegan. In order to have that Rinnegan, he need to implant a DNA from a descendant of the younger son who inherited his ancestor's power.
This is not evolution anymore, but pure synthesis or scientific manipulation. Just as Sharingan is the manifestation of a special chakra, Rinnegan is also the manifestation of Rikudo's chakra whether altered by Juubi or not.
These powers became one when Hagoromo was born and thus he awaken a new power, the Rinnegan. That is why the powers of both clans are needed in order to awaken the Rinnegan as it will give you the complete DNA and chakra set of Hagoromo Ōtsutsuki. A man which is a hybrid between the Juubi and humanity. Though this is only a very likely theory.
Whether the princess had power prior to eating the fruit is unknown. Whether her bloodline count in Rikudo's power is unknown. One thing is certain here: Rikudo's power prior to becoming a jinchuriki is unknown as far as Rinnegan is concern.
On the other hand, we know he beat Juubi by sealing it inside him. We still have to prove if he had Rinnegan.
The Rinnegan is formed and manifested in the eyes once the life force of the Senju Clan is added to the mix of the already existing Uchiha Clan power. The Sharingan is simply the manifestation of the Uchiha Clan's power. The added life force evolved the Sharingan into a Rinnegan, and thus its the natural evolution. The power of the Senju is their life force, the power of the Uchiha are their spiritual quality, their chakra. ( Again read my other thread for more info. )
You are wrong. It appears actually that the Rinnegan is actually a sign that someone has some kind of power or chakra inside him. Unlike the sharingan, the Rinnegan is solely performed with body part who have nothing to do with the eyes. In fact, Nagato was not even present when he was using the six paths of Pain. This tell you that the eyes themselves are for show.
Compare to Sharingan, the user need to maintain eye contact to perform genjutsu. Amaterasu come from the eyes, etc. The only Sharingan power that does not come from the eyes is Susanoo, and Madara proved it.
Finally,
you guys always ignore the Byakugan, which is also a dojutsus. It clearly proves that actually, the uchiha do not have all the bloodline of the elder son. Rather, they have something missing, and this explain logically why their eyes is not a spiral, and why it is red/black unlike the elder son.
Also, Jiraya based that off fairy tales and legends. They were proven wrong when Madara "created" the Rinnegan within himself as the Dojutsu didn't simply appear. Also, Madara never said you had to have the powers to open the Rinnegan. You need both powers in order to awaken the Rinnegan and to fully control the Gedo Mazou. Its also true that the Rinnegan is both Yin and Yang. The power of the Uchiha are the Yin, while the power of the Senju are the Yang. When these two powers are combined, they mix and evolve the Sharingan into the Rinnegan as a physical manifestation of the power's mixing.
First, Jiraya never said he was saying some fairy because he clearly identified the Rinnegan. Second, Madara never proved Jiraya wrong because Madara never awakened Rinnegan on his own.
By saying that he proved Jiraya wrong, you prove that you are in denial of the fact that Madara did not obtain Rinnegan the proper way. You deny that Rinnegan is a power that is rare as Jiraya said, awaken in all the history of shinobi by only a single person - Rikudo Sennin. Maybe, you need to ask Madara why he gave Nagato his eyes after awakening it.
Facts:
- Rinnegan and Sharingan are two separate and unrelated dojutsus. Madara proved it by Switching back and forth between Rinnegan and his EMS when he was revived
- Dojutsus are chakra generated by the body. Sharingan come from the brain, and Rinnegan certainly comes from both Senju chakra and Uchiha chakra. By switching between Rinnegan and Sharingan, Madara proved that he was loading two different type of chakra.