I strongly agree with the first one, and agree to a great extent with the second point as well. But I would present the third from a different angle: I think the Sake possibly had Sharingan or Sharingan-esque eyes as well. Think about it, Madara is as close to the sage as anyone can get and he holds the power to control the Bijuus and use the Sage's eyes as well.
Perhaps, as the lines were one, the sage originally had 9 Tomoe Sharingan with which he was able to connect and subjugate the Jubi and become its Jinchuriki. And just like Madara, he awoke the Rinnegan when he tore the Juubi from his body and created the moon and sealed it. It seems to be as if he used up its chakra to accomplish so, as the manga implies that when he was a Jinchuriki he was akin to a god, not without it.
In fact, the manga doesn't even talk about Izanagi - the technique of the Rinnegan to 'create' things - other than for the creation of the nine tailed beasts. It's quite plausible, he awoke his Rinnegan after the fused with the tailed beasts. The view of his eyes could just be a corruption of the story, as he passed on his mental energy - the actual energy of the self - to the older son and body to the younger one, and yet the older Son didn't seem to have a Rinnegan, but a strange spiral like formation.
Just my theory of course.