They're where I first heard about the Laid-Back Camp projects. Initially I was skeptical since I couldn't find an official source but then it got confirmed a while later. I'd say they're a good source.
Likely. (Which iy why I said unlikely, because not their own property.) Free has any chance to be slaughtered to the end of the world, as do Chuunibyou and Violet Evergarden, since those are all their own property. It's curious enough the Euphonium went with them, but that's a smaller publisher (somebody with say in the staff must have really loved it) and they appear to get a whole lot of freedom. Nevertheless there is still a small hope Hyouka might get picked up again, because somebody in the staff just happens to really like it.
But just commercially speaking Hyouka is probaly not the best pick up. =/