The rinnegan the sage of six paths had is different.

[LegendaryAce]

This is what I think happened

Sage had a dojutsu that was a rinnegan,byakugan then when he sealed the juubi it made a new dojutsu that mixed them all
And when he gave his elder son the eyes he had a watered down version of it ..explaining the spiral like shape we saw and when the son had kids it passed the hatred part of it to the son who was evil and passed hat was left to the Hyuga but what happened was the sharingan could unlock the ultimate power ..but it's not as strong as the original since its missing the last part

 

[Sexy Steel]

Then surely it would've worn of by now cuase he is dead.

well the gedo mazou is controlled by the rennigan and as we know the gedo mazou is the shell of the 10 tails, could be that madara is controlling it right about now with his rennigan taking into consideration that the 10 tails isn't full powered.