you may be interested in some tech details on that project's prototypes here:
https://www.quinnjh.net/projects/adaptive-instruments-projec...As for the tuning system, we didnt get great demo recordings of it, but the invisible strings were linearly mapped as a range onto degrees of a given scale. In our use-case (letting people with disabilities jam without too much dissonance) that key+scale and the master tempo were broadcast to each instrument.
Would have been interesting to play more with custom tunings, but the users we were designing for would have had a harder time using it consonantly. FWIW fully-abled folks like myself sound pretty bad on the theremin, and seeing people play them in orchestras etc displays an impressive level of "virtuosity" to place the hands properly. Quantizing the range of possible positions helps but the tradeoff is sacrificing expressivity.
As for 1) yes, there will definitely be some pitfalls with the relatively slow updates - which may show up as "zipper noise" artifacts in output.
For 2), logarithmic mapping between position and pitch is traditionally theremin-like, but as the theremin avoids zippering by being analog, youll have to get creative with some smoothing/lerping and potentially further quantization. Thats the fun and creative bit though!
Would love to hear about your project again and what approaches you take, and happy to answer other q's so feel free to drop me a line.