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The most important thing to remember in regards to soil is good drainage. As long as your soil drains well and is reasonbly healthy, your trees should do fine. To improve drainage and soil health, you can amend the soil with compost or other organic matter.

It is likely poor soil fertility than cross pollination. Cross pollination would affect the fruit of the tree grown from the seed of the cross pollinated fruit, not the fruit that was growing cross pollinated seeds.

Have your soil tested and adjust for anything that is off balance. Also make sure that your trees are regularly watered as irregular can also sometimes produce sour fruit.

Typically, leaf loss is due to irregular watering. These articles will help with watering and fertilizing your tree: https://www.gardeningknowhow.com/edible/fruits/citrus/tip-on-water-requirements-for-citrus-trees.htm
https://www.gardeningknowhow.com/edible/fruits/citrus/fertilizing-citrus-trees-best-practices-for-citrus-fertilizing.htm

Premature fruit drop is often the result of overbearing (which requires thinning), poor pollination or an insect problem.

This article may help: https://www.gardeningknowhow.com/edible/fruits/citrus/citrus-fruit-thick-rind.htm

Have you fertilized the tree? It may be lacking some type of nutrient. I would have your soil tested at your local extension office and then add some phosphorous to the soil to encourage blooming.

This article has fertilizing information that should help as well: https://www.gardeningknowhow.com/edible/fruits/citrus/fertilizing-citrus-trees-best-practices-for-citrus-fertilizing.htm

The trees are considered hardy in zones 8-11, though wrapping the tree or providing mulch for additional protection will help during winter if you are in a zone lower than 8, such as zone 7. Also, make sure that it receives plenty of sunlight and is well protected from winds. If it gets lower than 40 degrees F. (actually 50 F. would be pushing it), then you should definitely bring it indoors over winter.