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Neem oil will keep these pesky insects at bay. There are many other ways to do this as well. This collection of articles will give you more information, along with other good tips: https://www.gardeningknowhow.com/special/organic/

If you can dig out the stump, then this will be the best way. You can also pour boiling water on it every day until it is completely dead, but you will still be left with digging it out. The boiling water will make this easier.

Boxwoods are susceptible to a variety of diseases. "English boxwood decline" and Phytophthora root rot are causes of browning leaves. These are soil borne diseases that result in plant death. Other potential problems are outlined here: https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/yellow-or-brown-boxwoods.htm. Check the Arizona Cooperative Extension Service; they may have a bulletin on boxwoods or may offer diagnosis of plant problems.

You can use whatever tool works for the task and you! Make sure you sterilize the blades with alcohol before starting.
You can use lopping shears, hedge clippers, pruning saws, pruning shears and scissors!

Too much fertilizer is not good, as you know. Whether this was THE cause for browning leaves is not possible. When you fertilize, you must keep the plant watered. Fertilizers can build up in the soil to toxic levels. Not the nitrogen but the phosphorus and potassium. High levels of phos, inhibits the ability to absorb other nutrients, like calcium. 10-10-10 is fine for potted plants but too much for in-ground plants if used annually. Brown leaves are dead but the branches may still be alive. Before you fertilize again, get a soil test at your county extension service. But fertilizers are just the beginning. Boxwoods are prone to several diseases including "boxwood blight". Some others are reviewed here: https://www.gardeningknowhow.com/ornamental/shrubs/boxwood/yellow-or-brown-boxwoods.htm