Will the AF-S DX NIKKOR 35mm f/1.8G work with my camera body, the Nikon D3100?

A few months ago, my standard lens broke off the camera body and it would still work, but it wasn't always attached.

I recently invested in an AF NIKKOR 50mm f/1.8D without realizing that it would not enable Auto-Focus on my camera body… Oh, well, I will just have to practice manual focus for now!

Eventually, I might invest in a AF-S DX NIKKOR 35mm f/1.8G lens; it could be great for portraits but would it enable Auto-Focus on the Nikon D3100?

It will autofocus with your camera but you may not need to buy the 35mm at all. Your 50mm is better for portraits. Guess what? Manual focus is also better for portraits. You already have what you need.

The 35mm is better for general shooting since its standard/normal (focal length) for your camera. It is also good for whole body portraits and small group shots.

You should keep both. You never know when you might upgrade to full frame. The 35mm f1.8 DX is an EXCELLENT lens. You should be able to find it for under $200.