Holy black on a Po-Po... this thread is a mess.
"How can one be a blood relative without being descended from..."
That's simple. Because people are quaint and don't have functioning brains, they began to reason that the Senju started with the younger brother, and the Uchiha with the elder brother. Thus, when one says: "The Uzumaki were not descended from the Senju" - their brain cannot reason through the problem.
The solution is that the younger brother was neither Senju nor Uzumaki. Senju and Uzumaki lineages are branches from another lineage (which may or may not still exist - it's possible that their mutual ancestor could have become extinct).
As for the whole "The Sage started Ninja!"
This really isn't clear. He may have started the organized teaching of ninjutsu and other such things - but we see, quite clearly, that knowledge and ability to use chakra existed outside of the Shinobi systems (Samurai... remember those guys?).
So it can be reasoned that clans and different ninjutsu-like abilities existed before the Sage's time. The Sage, however, began the actual instruction that formed the basis of a Shinobi.
Which is what we will see when Hashirama explains to Sasuke: "What is a ninja?" The idea of a ninja was the Sage's theory on how to spread peace and discipline.
Thus all "conflicts" are resolved merely by changing the context in which the current facts have come to be.
