How do I select and mask and image as seen in the Black and White View Mode?

The first picture is the image. The second picture is a mask (where there's white the image will show and where it's black, the image will be hidden--think of it like where you shine a light. You can see in the light but not where it's dark). The third image is the original image with the mask applied. 

If you want to use the mask as the image, you can set Select and Mask to output to a Layer Mask where you can copy the layer mask and make it an actual image layer. Here's how:

1. Make your selection and go to Select and Mask to output to a Layer Mask
2. When you click OK, you'll see the image thumbnail with the black and white version to the right of it in the Layers panel as a layer mask.
3. Click on the layer mask (its thumbnail will be highlighted with white as opposed to the image thumbnail).
4. Do either of the following:
   • Go the Channels panel (Window > Channels), turn off the eyeballs for all channels, and turn it on for the layer mask
   • Or use Alt (Windows) / Option (macOS) + click on the layer mask to access the layer mask.
5. Select all (Select > Select All or Ctrl (Windows) / Command (macOS) + A) to select the black and white pixels of the layer mask and Copy (Edit > Copy or Ctrl (Windows) / Command (macOS) + C) it.
6. Do either of the folling based on what you did in step #4:
   • If you're in Channels, switch the visibility to what it was previously and go back to the Layers panel
   • Or if you're in the Layers panel, Alt (Windows) / Option (macOS) + click on the layer mask again.
7. Create a new layer and paste (Ctrl (Windows) / Command (macOS) + V).