There is no cost for storing the layer -- or using the layer. However, the layer storage does take up space in your total Lambda storage in your region (currently capped at 75GB).
Whether it's safe to host a public layer is relative. It depends on whether you want the data in the layer to be publicly viewable or not. The public layer will not incur you any cost if others use it.
There is not cost for sharing a layer.
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