Preparing the field (pgs 9-12):
You would think alchemy is not necessary to grow, because how do things naturally grow, or how did humanity survive when starting agriculture. Rather, I think it's a step to improve the yield. In normal farming you would apply fertilizer after sowing.
You can believe that every territory has alchemists because alchemy school is separate from the alchemy institute mentioned many times in the story, and is how those medallions are gotten, both the apprentice and master ones. Like the higher ups thought they might need a lot of alchemists so they created that school.