What's the purpose of the little white circle that appears in the center of a shape when I select the Free Transform tool? It doesn't seem to do anything.
That circle is the transform center point about which the shape will rotate when you rotate it. By editing the location of this circle, you can rotate an object around a point other than its visual center.
Why does my Brush tool appear to be working when I click and hold, but when I release, nothing has been painted?
You probably have the Brush tool's Brush Mode option set to Paint Selection, in which case only fills that were previously selected are painted. Other Brush Mode options can also cause unexpected results if they were set accidentally.
It looks like there are a bunch of other tools (especially those under the Options section) that we haven't looked at. Are we going to go through each one in detail?
Many of the rest of the tools and options are indeed covered where applicable in Hour 4. However, given the foundation this chapter has provided, you should feel comfortable exploring some of the other tools. For example, the Eraser tool has a modifier called Eraser Mode that's strikingly similar to the Brush Mode and Pencil Mode of other tools. Try to apply the knowledge you've gathered in this hour, and I bet you can figure out most of the other tools on your own.