I installed again Clean Backdrop, but I'm still having the same problems. I also tested all other plug-ins, downloading them again from the website, and these are the results:
Both Skin Mask and White Teeth worked well, with no apparent problems. (Although White Teeth took a longer time to process than any other).
Clean Backdrop and Fabric start normally, but when they load 100%, they crash and the AF closes completely.
For Dodge&Burn, Heal, Portrait Volume, Skin Tone, Eye Brilliance, and Eye Vessels nothing happens. But oddly enough, no window opened, nor was Affinity Photo frozen. It was as if I had already used the plug-in and was moving on with the retouching.
But regardless of Retouch4me's compatibility with AF, I'm very much interested in getting the software, and I'm sincerely thankful for your attention!