The purpose/meaning of buttons/icons in short
To a help page. Hover over the icon for the subject.
The wand reloads only the diagrams (faster) / the link reloads the entire page and your browser will remember the pattern
The character inside the circle determines the origins of the pairs used to make the stitch. The default cheat sheet shows all you need to assemble a pattern. An extended version shows additional symbols used in legacy patterns.
The Color-Code page explains colors and twist marks in general. Click the icon for an extract with actually used colors and stitches.
Resize space (not to be confused with zoom or patch size)
Depending on the browser/device, the diagrams may have a hot corner in the south-east, where the sliders meet. Drag this corner to adjust the available space. The buttons shown here are an alternative when the hot corner is not available, for example on touch devices.
It may bridge the difference in shapes of the holes between pattern definition and thread diagram. For example for dropped stitches or irregular holes. An example of the latter is the TesseLace pattern 3x4_447 which becomes surprisingly regular. See also reshape patterns.