When Madara dodged Sasuke's sword....Sasuke simply changed that outcome and replace it with the one he wanted via Izangai(which was to stab Madara with his sword).
No, He might enter into other dimensions of Rinnegan but not "Obito's Sharingan"
Kakashi stated that A pair of eyes have unique dimension.
And Kakashi is well known for his jutsu analysis.