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It sounds like you may have a fungus, though it is hard to say which one and many can cause this. Fortunately, all fungus can be treated with a fungicide. Treat the trees with a fungicide. I personally like neem oil as it will also treat for any pests the tree has and is safe for people and pets. Here is more information: https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

Brown rot is one of the most important diseases of peaches. To minimize brown rot spore populations, thin down or remove all remaining fruit from the tree. Fungicides are recommended as a preventative measure and should be applied during preharvest, as the fruit begins to color. Additionally, postharvest treatments, such as hot water treatments and chlorine dips, can sometimes be beneficial.

Here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/fruits/peach/common-peach-diseases.htm

This is peach leaf curl. This article will help:
https://www.gardeningknowhow.com/edible/fruits/peach/peach-leaf-curl.htm

This is a sign of peach borers. This article will help:
https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-borer.htm

This article will help: https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-fruit-drop.htm

This is very possible. This article will help:
https://extension.colostate.edu/pubs/insect/05566.html

I would also recommend that you treat the tree with neem oil. The neem oil gets inside the tree's system and will kill pests that other insecticides can't reach.