When Ayaka, Hiromi and Nino inform Mirai that they may have to eliminate youmu Akihito if they can't subdue him, she responds with 'dame desu' (You can't/bad/It won't work). It seems a little oddly worded... until you find out that Mirai's mission was to kill Akihito from the start, and her cursed blood is literally the only thing that can counter his powers.
The ending of episode 12 has heard a lot of cries of Ass Pull, but the reason Mirai disappeared was because she'd been sucked into the dimension created by Kyoukai no Kanata. Now that it was back inside Akihito, it's not hard to believe that she could be ejected from said dimension again - it just took some time for her to reform, so to speak.
One could even argue that she was just waiting for him to admit his feelings for her, just as she admitted her feelings for him just as Kyoukai no Kanata was disappearing. Wanting her there and admitting his feelings for her could have inadvertently caused her to escape the dimension.
Another argument is Beyond the Boundary is a Reality Warper. It just took time for it to recover enough energy to grant Akihiro's wish.
Simple but no less brilliant: Hiroomi's powers have the uncomfortable side effect of making him extremely sensitive to cold. He cools down quickly and has a hard time keeping warm. His weapon of choice is a scarf. Its probably the most effective and clever weapon choice in the whole show.
If Akihito is so dangerous, why are they tolerating his presence instead of killing him? Because they CAN'T. He's immortal and trying to kill him will just awaken his youmu side. It may be possible to imprison him, but that might give him a reason to go youmu and break through his captivity. The way things are, Akihito is surrounded by people who may or may not be forced to be with him out of necessity. It's a very unpleasant situation for everyone involved, but they all cover it up with pleasantries and random activities in the literature club.
