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This is a pollination issue. The tree will abort any fruit from flowers that were not pollinated. This has become an increasing problem with the decline of the honey bee.

These articles will help:
https://www.gardeningknowhow.com/garden-how-to/beneficial/insect-pollination-process.htm
https://www.gardeningknowhow.com/garden-how-to/beneficial/creating-a-pollinator-garden.htm

Though it may be a pain, if you want, in the future you can hand pollinate flowers. You can use a small paintbrush and gently swirl it around inside each flower. This will pollinate them.

These drought tolerant fruit trees typically bear fruit within their 3rd to 4th season—in rare cases, you could see fruit sooner. As they do not tolerate cold well, they are favorable to your area. Good, well-drained soil is probably one of the most important factors to consider when growing these fruit trees. This article will help: https://www.gardeningknowhow.com/edible/fruits/apricots/apricot-tree-growing.htm

The easiest method for the home gardener with only one or two trees are fruit spikes once a year in the early spring. They are driven into the ground around the drip line -the outer edges of the branches- and will slowly leach into the soil with each watering.

The grey could be a sign of fungal growth due to the over abundance of fruits, which can limit air circulation. Thinning the tree early on will help with this. In the mean time, treat with a fungicide, such as neem oil. These articles will help: https://www.gardeningknowhow.com/edible/fruits/apricots/apricot-tree-growing.htm
https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-thinning.htm

This is caused by uneven watering. It can happen when you have long periods of dry followed by a big rainfall. The plant is so thirsty that it sucks up water faster than it can grow and the fruit splits. To avoid this, make sure to water evenly and often. A drip system with a timer is a great way to avoid this.

These articles may help: https://www.gardeningknowhow.com/edible/fruits/apricots/apricot-tree-growing.htm
https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-thinning.htm (this would apply to apricots as well)

A number of things can cause premature fruit drop of apricots. The most common one is overbearing. When the fruit is pea size, begin thinning to prevent fruit drop. This will reduce the energy of the tree so it can put more into the production of fruit. If pollination fertilization is at too great a level for the tree to sustain, all of the set fruit will simply drop. You can also thin the blossoms rather than the fruit. The problem could also be poor pollination or fruit maggots inside the fruit.