Answer: Elm leaf beetles like elm leaves and don't usually bother other plants or trees. Likewise with the borers. Most are host specific so unless you have elm trees in your yard, they probably are not a concern. If the tree was sprayed with insecticides, there could be residual chemicals on the leaves which might harm your plants if the leaves fall on them. I'm afraid the only way to stop that is to rake the leaves rather than allow them to pile up near your plants. Sinking soil does sound serious, though. There may be a broken water pipe underground which is washing the soil away. Rotting roots will make the soil sink and settle but roots rot very slowly, not quickly and in 3 months you probably would not notice the amount of settling due to root rot. I'd have a professional check the area. They have the equipment necessary to locate water pipes. Best wishes with your landscape!
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