#1. "RE: D5100 + Nikon AF-S 35/1.8G autofocus problems" In response to In response to 0
I have such a lens and it has a manual focus override ring. If you have the time you sometimes need to hold the shutter button half way down to make autofocus work the manually adjust outside ring.
But another issue may the eye piece diopter adjustment you hold camera up to eye Glasses off (or own). and move the adjustment up or down until what you see is in sharpest focus. (I use Glasses off). (Doesn't necessarily have to be in focus. Just the sharpest focus.)