I read this story over twelve years ago. It was published with a lot of other stories (by the same author IIRC). The main story that I remember had to do with some kind of war games using pilots and mechanized units (not sure if mecha specifically or just armored vehicles) meant to resolve political issues without military action. While I think it's name was a year in the 1990's (ex. 1999) it could have been the name of another story in the collection or another decade. Later stories were much stranger, I remember something about a witch created by a mistake made by an AI and genetically modified humans with animalistic traits. I'm pretty sure this exists somewhere but every time I've looked I have not been able to find it. I'm hoping someone can help me, because I've always wanted to at least confirm it exists.
You should look for When the People Fell and We the Underpeople, both published by Baen Books around 2007. This is the complete Cordwainer Smith corpus, and will contain both stories that you've described - "War No. 81-Q" and "The Dead Lady of Clown Town" (the latter also available at the Internet Archive) - as well as all of his other stories, including his first published one, "Scanners Live In Vain" (also available at the Internet Archive), and his novella, Norstrilia.
Unfortunately, the e-book editions are no longer available for purchase from Baen; you'll have to look for used hardcopy.
This could be a book by Cordwainer Smith. The Underpeople were modified animals created as servants. One of his short stories concerned a girl created as a healer when the machine asked for information, and the (drunk) operator kept singing "....heal the pain"