Q.Peach and plum brown spot
I have removed fruit on trees and below. When and how to prune, sterilize utensils, fertilize, and spray for a better crop next season?
Wow, this question could actually lead to a short-course on peach and plum growing. I'll try to give you a few articles that will help you. First, there are at least two diseases that would come under the heading of "brown spot:" https://www.gardeningknowhow.com/edible/fruits/peach/peach-scab-treatment.htm
https://www.gardeningknowhow.com/edible/fruits/peach/brown-rot-fungus.htm
On the subject of pruning: https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-thinning.htm
https://www.gardeningknowhow.com/edible/fruits/plum/plum-tree-pruning.htm
You can sterilize tools by wiping them down with a cloth dampened with alcohol. The most important step to take toward a good crop is to maximize your cultural practices; in most cases, that means to give your trees the healthiest soil, best watering, and good light. Fertilizer comes in way behind soil and water. Here are articles on growing healthy trees:
https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-care.htm
https://www.gardeningknowhow.com/edible/fruits/plum/growing-plum-trees.htm
As a final word, I strongly advise you to seek assistance from the county extension service -- your tax dollars support them, so they are pleased to give you advice. This link will help you find one:
https://www.gardeningknowhow.com/garden-how-to/info/what-is-extension-service.htm