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It sounds like it may have been peach scab. This article will help: https://www.gardeningknowhow.com/edible/fruits/peach/peach-scab-treatment.htm

The only treatment is to minimize stress by supplying additional fertilizer and irrigation as well as removing some of the fruit load. Applying a fungicide in autumn will help prevent future problems. You can also try spraying some in spring prior to bud swelling. While it is often deemed to be less effective than fixed copper products, lime sulphur is an acceptable form of organic control for this disease. Here is an article that you may find helpful as well: https://www.gardeningknowhow.com/edible/fruits/peach/peach-leaf-curl.htm

Peach tree borers can also attack other pitted fruit-bearing trees, such as plum, cherry, nectarine and apricot, so these other trees (to the best of my knowledge) should be ok.

The gel is often a sign of peach borer. It may be dripping from the borer wounds. Borers can also affect plum trees. This article will help: https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-borer.htm

Yes, you can use Bayer Advanced Garden Tree and Shrub Insect Control for any borer issues. How well it work, I do not know. For additional information on controlling borers in peaches (and other fruit trees), here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-borer.htm

Splitting most commonly occurs in freezing weather. If the wound is not weeping or splitting further, then you should just leave it alone to heal on its own. If the split is widening or leaking as you say, you can try protective paper (sold at nurseries) to help hold it together while it heals. Do not cover the wound with tar or any other permanent substance as this can trap disease in the wound. It may also be attributed to peach tree borers. Here is an article that you may find helpful: https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-borer.htm