Why did Danzo lie to Hanzo?
In episode 347, Danzo and leaf anbu black ops transformed themselves into shinobi from the hidden stone village to attack the Akatsuki (Yahiko, Nagato, Konan). Nagato summoned the Gedo Statue to kill them. Danzo after brought the casualties to Hanzo and told Hanzo the Akatsuki are trying to take over the hidden rain village and are his enemies.
I don't understand this, why did the leaf ninja transform into stone ninja to fool Akatsuki and why did Danzo want Hanzo to turn on the Akatsuki?
Also, does the Rinnegan automatically allow someone to summon the gedo statue?
And lastly, why did Obito tell Nagato that Nagato was the reincarnation of the Six paths of pain if the eyes were originally Madara's?