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You can be assured that if your plants indeed have spiders, the spiders aren't the cause of any damage. Spiders eat insects, not plants. They would happily live on your plants if there were insects there for them to capture and eat, however.
OTOH, spider mites
do damage plants by sucking the sap. Spider mites create webs, too, but the mites are very small. You will need a magnifying glass to see them, and you will find them on the undersides of the leaves. The insecticidal soap should kill the mites, but you have to be sure you spray the plants thoroughly, especially the undersides of the leaves, as well as all the stems. You have to do repeat sprayings at 10 to 15 day intervals to kill any new mites that hatch. I usually find 3 sprayings sufficient, but it would probably depend on how badly infested your plants were. (That assumes, of course, that spider mites are even the cause of the problem.)
I'll have to leave the answers to your other questions for more knowledgeable members. I can think of a lot of different things that might
be causing the black leaves, but all I could really offer would just be a guess.