Nephytis (Syngonium podophyllum) is prone to root and stem rots if kept too wet. The soil should be allowed to dry a bit at the surface between waterings. There are also foliage diseases which may be what you are seeing, but the dying leaves may actually be a reflection of a problem in the roots.
I am not sure about the apparent feeding damage. This may be as it appears or it may be just where some diseased areas are now falling out of the leaves which happens, especially with bacterial diseases.
Trim out any affected foliage and allow the soil to dry between waterings. Keep the plant in a bright area out of direct sunlight and hold off on fertilizing until you see some new growth emerging.
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