Naruto, but the contract and summons are included with the Rinnegan. Most probably, though, it isn't even necessary.
2. I consider the Puppet aspects of Demon Realm (wielding one's body as a weapon, concealing traps/weapons within a body) to actually be beyond simply inspiration for ninja puppets. It's actually the original form of all ninja/chakra weapons and body manipulation. I suspect even the samurai method of wielding chakra didn't exist prior to the Rikudou, and every other technique that allows a ninja to alter his body using chakra (Oro's snakes, Suigetsu's water, Naruto/Bee's extra Bijuu limbs) are based on the way that Demon Realm works.
I consider most of the Path abilities (and possibly to a lesser extent the Sharingan abilities) to be the "pure" forms of ninjutsu, the most powerful and complete techniques. The reason they're only available to Doujutsu users is that only eyes such as the Sharingan/Rinnegan can grant the user such perfect knowledge of chakra control and ninja techniques.
Considering that each summon the Animal Realm path summoned had black stakes driven into them so that he could assume complete control over them, I suspect that would be the "contract" between them. There wouldn't really be a need for him to do all that if he had actual blood contracts with them, right?
If you mean the eyes that Madara had while he was still alive, they were transplanted into Nagato, and now Tobi possess's one of them in one of his eyes, the other probably hidden in his base. Im very sure this is the case because, as we know with Kakashi and Danzo, transplanted doujutsu eyes CANNOT be switched off. This is why Kakashi's covers his with his headband and Danzo did with bandages. Also, Shisui's eye that was in the crow implanted inside naruto did not turn back into a normal eye after the genjutsu was cast on itachi, it turned back to a sharingan eye.
Correct me if im wrong, but i have not seen a manga picture showing Nagato with normal eyes, its always with his Rinnengan turned on. Even in his death, his Rinnengan was still on. Now When Edo-Madara used the Rinnengan, we saw him switch from EMS to Rinnengan, something Nagato could not do. Edo-Madara could also use Susanoo and other Sharingan techniques while in the Rinnengan mode, did we see Nagato do this? nope.