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Peaches normally do not have a run of sap. If you are seeing a sap like substance, this can be one of 3 things. If the sap is clear and thick, the tree may have peach borers (https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-borer.htm), if the sap is amber, it may be peach canker (http://www.nysipm.cornell.edu/factsheets/treefruit/diseases/pc/pc.asp) or if the sap is clear, thin and dripping off the leaves, this is a pest infestation, likely aphids (https://www.gardeningknowhow.com/plant-problems/pests/homemade-aphid-control-a-natural-way-to-kill-aphids.htm) or scale (https://www.gardeningknowhow.com/plant-problems/pests/scale-bug-how-to-control-plant-scale.htm)

Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/trees/tgen/repairing-tree-bark-damage.htm

When pruning a peach tree, keep in mind that an open center is the best shape as this allows the sunlight to reach most of the branches. The best time of year to prune is in February once the danger of frost has passed but before any fruit has begun blooming.

First, cut off any dead or damaged limbs. Next, remove any branches growing towards the center of the tree as well as any downward-facing shoots. Also remove any small, thin shoots. Once blooming has begun, it may also help to pinch off some of the buds to induce more productive fruit.

I would leave it until after harvest if you can. While the risk is low on cutting a dead limb, any pruning can open the tree to disease, so better safe than sorry in case the plant purges the fruit to fight the disease.

First, cut off any dead or damaged limbs. Next, remove any branches growing towards the center of the tree, as well as any downward-facing shoots. Also remove any small, thin shoots. Once blooming has begun, it may also help to pinch off some of the buds to induce more productive fruit.

This is a disease called peach leaf curl. This article will help: http://www.ipm.ucdavis.edu/PMG/PESTNOTES/pn7426.html