Why does Edo Tensei Madara have Rinnegan? Edo Tensei restores a person the way they were at the time of their death. When Madara died, he was wrinkly and old. How come Edo Tensei Madara is brand new?
Rinnegan is not a kekkei genkai/tota. Why does Edo Tensei Madara still possess the Rinnegan when, at the time of his death, he wasn't possessing Rinnegan (because he implanted them onto Nagato)? 
Madara lost vision in one eye due to usage of Izanagi, but after awakening the Rinnegan, was he able to restore his Eternal Mangekyou Sharingan that he lost?
First of all, the Edo Tensei doesn't just restores the body at the exactly time of death, but it does it as if it was brand new, the body is kind like 'reborn'. We see it on how: 


Edo Tensei Deidara had both eyes instead of his robot left eye;
Edo Tensei Sasori had a 'human' body instead of a puppet one;
Edo Tensei Nagato had his Rinnegans even tho Tobi had taken his eyes from his body; 
Edo Tensei itachi had his Sharingans even tho they were transplanted on Sasuke.


Now when it comes to Madara, Kabuto had aprimorated the Edo Tensei Jutso so when he brought Madara back to life he was younger and stronger than he was when he died.

Here's the image after he showed everyone that he has a pair of Rinnegan. Kabuto mentions that he made modifications to the body.