Read-along video #3 suggest to me that the war was already underway before the story started, which would explain why the TV was showing images of bombs to begin with. The house and the lab were already in some remote location, thought to be safe.
What killed the original Mion? I think that's deliberately left vague, but it was whatever broke the window in memory sprout #5. The window returns as recurring imagery in 4-1 in the background of some rooms; in one room, it's obscured by glitches. A traumatic, repressed memory?
After Mion's death, the war seems to intensify, shown by the frequency of bomb images on TV.
How is "Mion" observing the creation of the horned Mion? I think you're right that hornless Mion floating in the void is the "red" Mion at the end of the game, but I don't think it's supernatural. This is the uploaded copy of Mion's mind that was shut down in memory sprout #9, which is why hornless Mion visibly glitches out right at the end. The shimmering blue wall that blocks her from entering the room - which disappears at the end of #10 allowing you to enter the room - represents some kind of barrier between the computer world and the real world.
Why does original Mion see horned Mion as a blob? Hard to say. Maybe it's some kind of imperfection in the Mion copies, and this is what it looks like in its imperfect "digital" form.
What happens in memory sprout #11? My theory is that original Mion, somehow entering the real world, tries to interact with everyone just as before (through machinery?) but instead inadvertently kills them. This somehow causes copies of mom and dad's minds to be uploaded as well in the form of Lumen and Umbra. It's no mistake that when original Mion sees the real world again, there are bloodstains leading through the walls and into the void. Horned Mion gets disabled at this point as well.
What is going on in memory sprout #12? I think there was some kind of process for creating more copies of Mions, after the first success. Of course, all these were also imperfect copies. The system was full of them, and original Mion was stuck in an endless cycle of destroying untold imperfect Mion copies for a long time.
I think the starting room of the game is actually where newly assembled Mion copies are placed, and that new horned Mions have been popping up in this room for centuries before the game started. Somehow they get destroyed through a combination of the deteriorating facility, the shadows and hostile plant life, and original Mion's actions, which accounts for all the dead Mions you find later in the game. It is possible that Lumen and Umbra, somehow manifesting to each new horned Mion, have been doing this for the entire time.
I can't explain what the shadows are. Probably intended to be the ghosts of the dead - the artbook hints that boss #1 has some kind of connection to Mion. Boss #1 must be the corgi, which explains his appearance and his persistence in following Mion.
The machines, on the other hand, are probably controlled by original Mion. Boss #2 is clearly a bigger version of a prototype in mom's lab in memory sprout #3.
The plants are obviously dad's work as seen in memory sprout #2, rampantly growing over everything.
What does the divergence between the normal ending and the true ending mean? Memory sprout #13 shows that original Mion locked the big door (behind which her uploaded mind is stored) and hid the "key" in the house. She clearly has physical access to these places. This sequence of events also suggests that the path you take in 3-3 when you can't unlock the door leads directly to the house. When you take the route to the normal ending, that means that you failed to find the "key." However, original Mion clearly did not leave the key for horned Mion's benefit.
I suspect the "key" was a message for Lumen and Umbra, in order to restore their memories so that they know what needs to be done. This is why you are able to use the key in chapter 3 even though you only find it in chapter 4 - the "data" was carried over by Lumen and Umbra from a previous cycle. Original Mion's plan was to leave this to lead Lumen and Umbra to find her and bring her a new body.
What happens when you fail to find the key? You end up in chapter 4. My interpretation is that none of chapter 4 is real; you are now in original Mion's trap, and you are experiencing some kind of virtual world that cannot possibly exist in reality (how could 4-1 be real?). This is why there are now glitches in the world you are experiencing.
The start of chapter 4 suggests that you have actually reached the real house, but the end of chapter 4 - there's a machine there with a monitor, and some puppets - suggests that "mom," "dad," and the corgi as seen by horned Mion in the house were actually these stand-ins being controlled by original Mion. By the end of chapter 4, you have become just another copy that original Mion has succeeded in destroying. Lumen and Umbra are left behind to start the cycle over again. If they happened to find the "key" along the way, however, that will open the path to the true ending and finally break this cycle.
In other words - another Japanese game where you are trapped in an endless cycle of events until you break out of it. At least that's my theory, but it seems to fit this structure that's incredibly popular in Japan for some reason.