THe black soot is growing on honeydew, a substance excreted by certain insects such as aphids, whitefies and scale. If you discover the insect then a treatment suggestion can be made. White spots beneath the leaves sound a bit like whitefly pupae. The falling leaves is a sign of stress perhaps due to the insects or perhaps because of dry soil conditions or even poory drained soil conditions.
I suggest you take a sample from the plant to your County Extension Office for help in identifying the insects and for appropriate control options.
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