I have never noticed any difference for displacement. Photoshop seems saves only 16 bit HAlf float exrs anyway but 16 bit integer always worked fine for me too
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Depends on the compression format of the normal map for sure, however if you are using DXN (BC5) with a 16 bit aware compressor and 16 bit normalmap source files then there is next to no gradients that will cause a visible compression artifact.
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Switching to 16 bit will double the number of bands, but decrease the contrast between bands. If the gradient takes place over a larger number of pixels than bands, there will still be visible banding, even in 16 bit. Have you tried converting the normal maps to 8 bit after exporting the 16 bit image? This will introduce…