Does the mouse pointer become different shapes depending on the pointer's location and locations you click on the screen?

Yes and no. It really depends on what the programmer decides. A GUI interface is usually composed of many objects, some of which may be part of the operating system's development kit (common controls), some of which may be user-defined and others which may be defined by a third-party. However, all objects respond to messages whenever a mouse cursor enters or leaves an object, or otherwise interacts with the object (moves or clicks upon the object). A programmer can intercept these messages and decide how the cursor should change, if at all.