Several issues here:

Peach Leaf Curl, too late to prevent it this year. Pick off those diseased leaves and destroy them. During a dormant season, spray the tree with copper. Copper is used as fungicide here.

Peaches have many pests that attack fruit since they are tiny. The serious pests are Oriental Fruit moths, Plum Curculios and codling moths. They usually lay eggs on fruit, larvae hatched and tunnel inside the fruit to feed. Fruit drop prematurely. These moths breed in soil under the trees. You need to pick up all those dropped fruit and throw them out with trash. You need insecticide for it.

Ripe peaches can also get brown rot. Another fungicide is needed.

oozing at the base of the tree could be a peach borer issue. Clean out the jelly substance, look for holes at the base of the tree, sometimes a bit below a soil line and use a wire to poke the holes and kill the borers. Insecticide is needed..

You can look up university extension services near you and read up on these problems and how to treat them.

There are more organic way to treat these issues. They often is more labor intensive with less effectiveness.

The spotting and then rotting is called brown rot. It needs to be treated with fungicide early. Dispose of all the "mummified" fruit and any fruit that falls off. The old fruit will produce spores that spread the brown rot. Monterey fungi fighter has worked well for me. There may not be much you can do this year. Once the peach gets the brown rot, fungicide will not stop it.