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This article will give you some tips on general fruit tree spraying for preventive maintenance: https://www.gardeningknowhow.com/edible/fruits/fegen/fruit-tree-spraying.htm

The information you need is in Table 2 in this article: https://aggie-horticulture.tamu.edu/syllabi/325/schedule/Pest%20Management/Chemical%20Application%20&%20Safety/Malathion%205EC.pdf (PDF)

Dormant sprays should actually be started in winter. Use dormant sprays before green tissue shows in spring buds. Use on days when the air temperature is above freezing. Use a Superior Oil spray for the first dormant spray application in mid- to late winter. Three weeks later make a second application of Superior Oil or Liquid Lime Sulfur. When spraying trees to control peach borer pests, choose those with lindane endosufan or chlorpyrifos. Sprays should be mixed according to label instructions. They should also be applied so that it runs down the trunk and soaks into the ground around the base. Try not to spray on foliage or any fruit that may still be on the tree. The best time to spray trees is within the first or second week of July and again in late August or September.

The tree should be fine. Don't put anything on it as this can cause more harm than good. Tree wounds will generally heal themselves. The following article should be of some help to you: https://www.gardeningknowhow.com/ornamental/trees/tgen/repairing-tree-bark-damage.htm

This article should help: https://www.gardeningknowhow.com/edible/fruits/peach/tree-with-no-peaches.htm

Yes, you could use neem oil. It's both an effective (and safe) insecticide and fungicide. Here is more information: https://www.gardeningknowhow.com/problems/pests/neem-oil-uses.htm