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The cold will kill the blossoms. The tree can survive colder temperatures, but the fruit will not form unless it has a long enough time to ripen. I'm afraid covering them won't prevent the cold from damaging blossoms. These articles will give you more information on the care of the tree: https://www.gardeningknowhow.com/edible/fruits/loquat/

Temperature changes, a drop to 25F will cause fruit to drop,
The green apple aphid (Aphis pomi) and the codling moth (Cydia pomonella) infest loquat trees in California will cause fruit drop.
Fire blight (Erwinia amylovora), spread by bees, attacks loquat trees in areas of high humidity or that have late spring and summer rain.
Fertilizing recommendations vary. Some authorities say they should be fertilized once a year in mid-winter. For each tree 8 to 10 feet tall, the California Rare Fruit Growers Association recommends applying 1 pound of 6-6-6 fertilizer three times a year when the trees are actively growing.

https://www.gardeningknowhow.com/edible/fruits/loquat/growing-loquat-fruit.htm

At most, even the largest species will only get about 35 feet tall. It could be likely that this variety is that of a shorter specimen. If you are taking care of it as you should, then it will grow to its maximum height on its own. If it gets wider, and not taller, then this could mean that the tree has already reached its max height. Here is an article for more information: https://www.gardeningknowhow.com/edible/fruits/loquat/growing-loquat-fruit.htm

I unable to identify the pest, as we do not have those around here, but I can tell you a solution that will work for a broad range of insects.

Boil some sliced hot peppers in water, and let this cool and strain. Mix in neem oil, garlic extract, and rosemary oil. Spray this and it will keep just about any insect away.

This collection of articles will give you more ideas on making your own pest control, as well as many other gardening tips: https://www.gardeningknowhow.com/special/organic/

If it does not have enough time to dry out, almost completely, then it can cause an infection. As long as it is not too far gone, you can apply dolomitic lime, and wettable sulfur around the tree out to about 1 or 2 feet from the trunk. This will kill off as much as the infection as possible in the soil, so that the tree can start to recover.

Make sure to only water when it needs it, or when it stays dry for too long. They can handle a little drought, but they will need water when it stays dry.

This article will help: https://www.gardeningknowhow.com/edible/fruits/loquat/growing-loquat-fruit.htm

This article will help you.

https://www.gardeningknowhow.com/edible/fruits/loquat/getting-a-loquat-tree-to-bloom.htm