Answer: I think you are dealing with two separate issues here. The black (actually dark purple) coloration where the stems branch out is normal on pepper plants. If it were a disease it would not be confined to just those areas of the plant. Instead it would be all over the plant, including the leaves. Some pepper varieties have more pronounced purple coloring at the nodes. It is perfectly normal on pepper plants.
As for the flowers falling off without developing into a pepper, lack of pollination is the cause. Insects must visit the flowers to transfer pollen. If they don't the flower will either not produce fruit or will start to form a fruit which will fall off while it is still tiny. Cold nights (under 55F) and/or hot days (over 90F) can also prevent flowers from forming fruits. As the summer progresses, your plants get bigger and have more flowers, and there is more insect activity in your garden, your pepper plants will develop peppers. Good luck with your garden.
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