Also check 
I like Denji and Asa moments! I like how she was expecting him to not actually try to kill her so quickly.
Now, this transfer students can be many things. Death, Control or some other horseman. I mean, I leaning towards Death since it would feel weird for Control to comeback a 3rd time shortly after Nayuta's "death" and another horseman would feel like the story is trying to pad out time for the actual Death.
As for Yoru's Plan, I am pretty sure the whole killing Death thing is just so no one can die and those can create infinte conflict in the world which would inadvertently make her the most powerful devil that has been killed before.
Can't wait to see where this goes!