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No, fertilizing didn't cause fruit to fall. This article will give you some new insights: https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-fruit-drop.htm
Yours is a very young tree. To the tree's way of thinking, it's just not ready to handle all that fruit. It needs to spend its energy on growing roots, so that it can support fruit in a few more seasons. By the way, fertilizer spikes are not very popular with experienced gardners, although you had the right idea to dissolve them in water first. Use fertilizer as described in the article.

It sounds like it may be a pollination problem. Without pollination, the flowers cannot form fruit. You can hand pollinate in the future by swirling a small paintbrush in each blossom. Here is some information you might find helpful: https://www.gardeningknowhow.com/garden-how-to/beneficial/insect-pollination-process.htm, https://www.gardeningknowhow.com/garden-how-to/beneficial/creating-a-pollinator-garden.htm

Sounds like peach borers may be your problem. Here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-borer.htm

It could. It is hard to say, as conditions like water runoff would affect how it effects your soil. Really, if I were you, I would have your soil tested. Here is more information on what that entails and where you can have it done: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-soil.htm

This sounds like it could be Oriental Fruit Moth. This article tells you all about these pests: http://www.ipm.ucdavis.edu/PMG/r602300211.html
The best idea is to take some samples of infected fruit to the local Extension Service for analysis and recommendations for control. This link will help you locate one: https://www.gardeningknowhow.com/extension-search/

In peach trees, this can indicate a root problem. I would check around the roots for signs of root rot. This article may also be helpful: https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-leafing-problems.htm Additionally, some trees, like peaches, may be slow to start if they do not receive an adequate chilling period in winter. Here is more information: https://www.gardeningknowhow.com/edible/fruits/peach/peach-chill-hours.htm