What's your question? Ask

Technically, peach and nectarine are the same fruit. There is literally only one gene difference between the two (which results in a fuzzy or non-fuzzy fruit). Beyond this, cross pollination only affects the seeds (the fruit of tree planted from the seed would be affected). It is only something you need to worry about if you plan on growing trees from the peach or nectarine seeds.

Some popular dwarf varieties are; El Dorado, Golden Gem, Southern Sweet,
Bonanza II, Southern Flame, Southern Rose, and Garden Gold.

https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-care.htm

Your tree likely has Plum curculio infestation.
Peach Trees can be infested with this beetle.

Here is a link with more information.

https://www.gardeningknowhow.com/edible/fruits/plum/plum-curculio.htm

There are different reasons and different methods to thin a Peach Tree.

Here is an excellent article that will help you decide the technique that will work best for you.

https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-thinning.htm

Diseases of Peaches or stone fruits can be caused by bacteria, fungus or virus.
I do think that your peaches may have Powdery Mildew, as this generally shows up on young peaches as small spots, then it spreads. You would also see the Powdery Mildew on leaves.

Inspect the tree for any other evidence to help make a correct diagnosis.
Keep in mind that nutritional issues could also cause some tree and fruit damage.
Here are some articles that will help you.

https://www.gardeningknowhow.com/edible/fruits/peach/common-peach-diseases.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, 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.