If I'm remembering correctly, googly eyes results when you replace the default eye mesh and then have another mod that's trying to map textures onto it that no longer show up in proper alignment. I use Comprehensive Style Collection, and this will happen to me on certain NPCs if I try to use, say, Cobl Races cosmetic stuff. So basically you've got two mods conflicting in this regard. You should post your load order so it can be determined what other mod might be modifying eye textures. Also I'm sure someone more knowledgeable can better explain exactly what's going on, I'm not sure my explanation for the problem is technically correct, but it's definitely a conflict.
I'm not sure about the hair issue--I'm not familiar with Head 06 (I'm assuming it isn't at fault when it comes to the googly eyes but I don't really know for sure), or how it might be causing a conflict. I haven't tried to play with it since way back when I installed CSC but I believe the hair showed up for me in the character creation menu just fine after installing it.