@RunaVolkov
One of the cases was the killing of many innocent civilians on a technicality
It's very arguable that it wasn't just a "technicality" since the Francois were the ones who broke the rules first. The Francois purposefully incited, armed and militarized the Arene civilians with the explicit intent of using them as shields, believing the Empire would feel tied up. That itself was a blatant violation of the rules of war, and such things are generally quid pro quos. IRL it is a violation for an attacker to bomb a hospital for example. But that's dependent on defenders also obeying that and not using hospitals a military bases. "Laws of War" aren't a magic shield, they're mutually agreed upon ways to stop a race to the bottom in all side's interests. But if defenders go ahead and make a bunker and garrison troops in the basement then say "nyah nyah can't get us because there are patients above us", well some countries might try to hold back anyway if they can afford to. But can't act shocked if they don't.
I’ve forgotten how the war started
Legadonia started it with a border violation (c14 pg20), it's an important plot point that everyone was really pissed at them but didn't want them to fall for realpolitik reasons. And just like in WW1, webs of treaties, lack of trust, perceived national interest, and nobody really understanding how modern industrialized war would change things, slowly sucked in more and more players. World War wasn't ultimately in anyone's interest, it was stupid, but humanity does stupid stuff sometimes.
Of course history is written by the winners and the Empire lost, though maybe they managed a negotiated surrender (not a spoiler genuinely speculating, LN doesn't go that far yet so who knows how the final will play out). A lot of details of the war were covered up, remember we saw records of Arene destroyed by Kingdom intelligence agents because of the propaganda issue. The commies of course did enormous amounts of propaganda too, and so did the Allies (Tanya and her wing's existence seems to have been wiped from the official records). The Empire got vilified, though that's pretty normal in war.