I don't know if this issue is limited to my M&P 22c (purchased 3-4 years ago) or if there was an ongoing problem, but the barrel in mine leads up badly if I use cheap ammo that isn't copper washed. I now only use CCI Mini Mags or Remington Golden Bullets, which will still lead the bore eventually but it takes a lot longer than with plain lead bullets.

As for dry-firing a .22 pistol, it's like running a car engine past the red line. Once or twice won't ruin it, but don't make a habit of it.