Madara said they couldn't leave the way they were so I'm thinking Madara somehow managed to off Rin with an uber jutsu from the distance (couldn't be that hard) thus freeing Obito with the newly unlocked Kamui. Maybe he sent a Zetsu to do it?
obito said kakashi let her die so maybe she died i the war or on some random mission we won't know though until its explained in the manga there may even be a flashback on it.
I think Obito killed Rin and Kakashi didnt do anything about it so Obito got pissed, other than that I think Kishi has a big surprise coming for us that will leave us shocked