This is great, thank you.
When I play-tested the game, I did it in a digital canvas tool (Figma) which let me paste in the grid image from the rules, and then move virtual pieces around to keep track of combatants. I think a chess board is a good way to do this in the real world, or if you print out the grids and use tokens/pieces of paper. Not quite as "pen-and-paper" as it could be.
I hadn't thought much about the difficulty of combat. I didn't want it to feel unfair, but that's about it. Let me know if you consistently win battles, and maybe I'll think about ways to make it harder.
I've updated the PDF to fix those typos. Well-spotted.