We aren't told how the Senju and Uzamaki are related. The Sage isn't a god. He is a human, that means he has parents. We don't know the Sages name, but what if it was "Uzamaki-something"? That would make Naruto a descendant of the Sage, it would also make him related to the Senju.
Kurama only said that Sasuke has a sinister chakra like Madara. Naruto refers to Sasuke as a brother, because he has a strong bond with him. If what you're saying is true, why doesn't Madara refer to Harashima as his "brother"? And it's just not them that can "enter" each others minds. If you read it properly, Sasuke says "high level shinobi" have the abiltiy to read/feel each others heart.
Imo, he is the Sages reincarnation. That's why all the Tailed Beasts recognizes his as the reincarnation of the Sage.
"You all think it as well...right?" "Naruto is the old man's..."
You must be registered for see links