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There are many reasons why peppers may drop fruit. This article is on peppers dropping flower buds, but the reasons listed in this article are also the same as what may cause pepper fruit to drop: https://www.gardeningknowhow.com/edible/vegetables/pepper/pepper-blossoms-falling-off.htm

The spots on the peppers may be sunscald, which is like a sunburn for plants (especially if they're more toward the top). While they should recover on their own, providing them with some shade will help correct this problem, especially if it's been really hot lately. We recommend shading the pepper plant with a translucent cloth cover.

If the rotted spots are at the bottom part of the fruit, then it's likely blossom rot. Here is more information: https://www.gardeningknowhow.com/edible/vegetables/pepper/pepper-blossom-end-rot.htm

The following article(s) should be of some help to you: https://www.gardeningknowhow.com/edible/vegetables/pepper/how-to-grow-red-peppers.htm

I have not heard of this before but if the plants and fruit are healthy otherwise, I don't think it's anything too serious. Just clean the peppers good prior to eating and they should be fine.

A simple inexpensive solution is to use a mixture of dish liquid and some vegetable oil and spray on the affected areas, after removing old/yellowed leaves. Similarly, a solution of vinegar and water, bleach and water, baking soda and water or garlic boiled in water may also be effective.

Bell peppers often have a purple-black coloration at points where stems meet, so this would be normal. But if the black color is a solid black and the area is shriveled or mushy, this would indicate an issue. As long as your plant is healthy and thriving, however, it should be fine.