Layers showing as checkerboards after 0

Hello. I'm trying to make layers, but I'm having three problems. First, when I use the polygonal lasso tool to make a layer, it only makes straight lines and therefore
rectangles. Is there a way to separate other shapes? See 3rd screenshot.

The second problem is that when I double click an area to select it, it gets messed up. See 1st screenshot. Is double clicking not right? I read it in a tutorial posted below.

The third problem is that the layers after 0 show as checkerboards. See 2rd screenshot. Is that how they're supposed to look?

Thanks in advance for answers. Here's the tutorial I used.

1. 1. Right-click
   the lasso icon in the Photoshop toolbox and then click "Polygonal lasso
   tool."
2. 2. Click each
   corner of the piece that you want to separate and then double-click to select
   the area that you have outlined.
3. 3. Click
   "Layers" in the menu bar and click "New" to open a new
   cascading menu.
4. 4. Click
   "Layer" to split off the selected part of the image as a new piece.
5. 5. Repeat
   this process for other pieces