The main character of this series is heavily implied to be that girl who committed suicide in the one shot released right before this series began. The last thing she says to her girlfriend before she says goodbye is she wants to be a shimeji mushroom so she won't feel lonely.
I'm pretty sure that Shijima is actually a version of the other girl from the one-shot, considering she more closely resembles her and both have an inventor sister. The shimeji mushrooms themselves are probably what embody the dead girl. Regardless, I doubt the one-shot will be treated as 100% canon to the series, though elements of it will likely carry over in some form. Like, maybe the girl that Shijima remembered playing with when she was little could be a version of "Yocchan."
As for the cause of the glitches, it seems like Shijima's sister has stretched the fabric of their reality so much that it has nearly broken. The first noticeable glitches occurred back when Shijima and Majime returned from that dream world, right? The bottomless hole was also a sort of glitch caused by her inventions.
It's been a while since I read through the earlier chapters, but does it seem to anyone else like the panel layout is changing in a kind of 'glitchy' way?