We didn't actually controlled Rin, he pulled an Aizen on the whole situation.
We don't have a chapter of Madara doing it but we have his words..
Naa, he wasn't in a genjutsu and he didn't see Kakashi killing Rin before it happened. He saw what Kakashi saw with the Sharingan, at the same time. Remember, when Obito arrived, Kakashi had already stabbed her. The stab itself happened when Obito got the images from Kakashi's eye.
We don't know. But it must have been the eye from a nameless, unknown Uchiha. In times of war it should've been easy for Madara or Zetsu to get a sharingan from a dead body.
No, both of Izuna's eyes (which Madara had transplanted into his head) turned into Rinnegan. Even the one that got blind after the usage of Izanagi was repaired in this process. He then implanted Izuna's eyes into Nagato at some point in time. After that, Madara implanted the single normal sharingan into his own head.
(1) Obito wasn't in a Genjutsu; he was seeing through his Sharingan that was currently implanted in Kakashi. He didn't see Kakashi kill Rin prior to her death; he merely saw Kakashi kill Rin through Kakashi's Sharingan first, and then Obito himself actually reached the scene and confirmed it with his own eye.
