Hello, so actually in the game around the end of Sakura's route, you find out that Aoi killed his farther after his father came to deliver poison to Aoi and also make Aoi tell him where Shino(the mother) went. She was already dead of course, but the father didn't know. Sakura hid the body of the father under his dorm bed. That was probably the only part of the story that didn't have a clear resolution, however we can probably just make up what we think happened to the body.
As for Narumi and Kamiya... using context clues and the fact that the professor looked old, like 50's or 60, similar age to the grandpa/father(kanata), and also the fact he said "two prodigies: one died and one disappeared". ... We know the one that died refers to Kanata, the reason why is because he was still known to the public and also the professor didn't know about Aoi. However the one that disappeared, my best guess is that it might have been Kyoya. Since that is the only other character that we get any bit of backstory of and it wouldn't be unlikely that he too was a prodigy but succumbed to the mental trauma his father instilled in him. So my guess is that Narumi was Kanata's first wife that bore his 3 sons (the youngest seems to be Kyoya). The professor could probably have been a friend or classmate of Kanata, since they would have been around the same age.