I can confirm that I cannot paste anything in that drawing that I copied from that drawing. I can, however, paste something into that drawing that I copied from another. (I ain't about to try it the other way, I've never seen something like this and I don't want the same problem!)
If I erase everything on the "9" layer, I'm also unable to copy to clipboard, so I'd imagine it's something to do with entities on that layer, but maybe that's just another problem.
I've had problems with drawings with a lot of layout sheets, but not of this variety. I noticed you had a lot of sheets, so I tried to eliminate that as a potential culprit. (The best practices, albeit from 2011, says to use ten layout max.) But I erased all the layouts and audited and purged and got the same thing.
I thought maybe that you're drawing units were all screwed up since you're using metric, but then I realized you're south of the border (I'm in Alaska), so that looks okay.
Sorry I couldn't be of more help, but I wanted to let you know about the layer 9 thing.