Yeah he did, it was originally madara's, who gave it to Tobi to make sure he was revived with Rinne of Rebirth
Zetsu is the supervisor of this whole process
Did tobi gave rinnegan , as he clames, to nagato randomly ?
Yeah he did, we just don't know the circumstances for it, they are Madara's rinnegan and the plan was that they would eventually be used to revive him, Nagato used it on Konoha, dying in the process, meaning the plan was ruined until Edo Madara came around.
Yeah he did, it was originally madara's, who gave it to Tobi to make sure he was revived with Rinne of Rebirth
Zetsu is the supervisor of this whole process
He gave nagato it because he is an uzumaki(senju blood). Senju + Uchiha= SO6P. Its All to control the ten tails.