16 steps...? A traditional 6stage attenuator has 64 steps, so if each step is 1dB you get down to -64dB, should be plenty. If you need more steps you will have to accept more switches in the signal path which is not good for sound quality...
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Is there ideally an exponential or a linear relation between the Gray code and the gain (with gain < 1, of course)? As the patent is a DAC patent, I expected linear.
Oh, so it's not about the number of steps, it's about the size of the steps - yes, you are right to raise that point: but I don't know the answer...
The linear pot scale should translate into a log attenuation curve. Is this taken into account with most relay attenuators?
Negligible I would say. All professional audio before digital put signals through dozens of opamps quite happily. You might want to checkout this thread of mine too: https://www.diyaudio.com/community/threads/12-opamps-chained-measurements.346722/
In fact the art of analog signal processing is in using enough active devices to correct for or avoid the failings of passive components, be it gain loss, impedance issues, noise, non-linearity (ie inductors, large value capacitors). This might seem counter-intituitive till you actually try doing design for real, for instance a low noise differential line-input circuit (where 3+ opamp designs out perform the single opamp considerably).