Yes, a child attempts suicide. This happens in the episode labeled season 2 episode 22 in Crunchyroll, but the labeling of the seasons seems to be funky so it might be different if you’re watching on another site/on dvd
In episode 4 around the 12 minute mark a boar is caught in a trap and then killed, there is blood. In the same episode around the 16 minute mark 3 foxes are shown to be dead, there is no blood.
In episode 5 around the 4 minute mark a bird is decapitated, there is blood.
Not destroyed, but in episode 2 during a flashback a much younger Kage has a gift toy car given to him by his mother, which he has to trade for an apple so he doesn't starve. He is beaten up and the apple is taken back, but he doesn't get his toy car back.