With 8 bit ProPhoto one would expect more rounding errors since the color steps between one bit increments in rendered values are greater in ProPhotoRGB than sRGB.
Yes,
after the initial rendering to each, from high bit data. I still have to dig up the tests and dE reports doing this when setting LR to save out 24-bit data. But I suspect it will produce the same results (unless Dither is added which Photoshop would do and LR doesn't with high bit export). After the rendering, yes, you would ideally want to edit the wider gamut, any gamut data, in high bit.