I do know that there have been other discussions over the HQ mod but I have been searching for weeks and have failed to find one that even comes close to the issues I've been having. None of them had ...
It's my understanding that the HQ mod requires a gaming quality graphics card to run properly. This is what Alf-Si says about your problem:
4.1. If sim (or part of it) get black textures (example), it means there is incorrect shadow (sometimes - diffuse) map. If you want to find it, you need to change all wearable things by sim to standard stuff from basegame - skin/clothes/tattoos/hair/makeup/etc.