It's possible Madara escaped death through Izanagi. He had given his eyes to Nagato, or so people presume, and took two sharingan eyes from somewhere, and him escaping death would be the use of izanagi which is why he probably doesn't have that right eye.
As for giving Nagato the rinnegan, I highly doubt it because if Nagato had Madara's rinnegan, he would've been able to switch to eternal mangekyou or regular sharingan to utilize genjutsu, susano'o, amaterasu, and tsukuyomi, and any other sharingan techniques like copying techniques (which the rinnegan would be better at).