In response to your first question, you can use the MouseMove event. This event handles whenever the mouse moves and passes in the coordinates of the mouse. With it you can determine the location of the mouse and if it has an X coordinate of less than 300 and a Y coordinate less than 300, you can change the color of the button (lookup the property of the button called BackColor).
For your second question, you seem to be asking about drag and drop. There is a nice article that can show you the basics here...
vb-helper.com - Drag and Drop exampleThe idea is to start a DoDragDrop on the control and on your target setup a DragDrop event to then accept the drag content and do whatever you want with it.
The last question... as far as moving the group box, it is the same as any other control. You can set the "left" and "top" properties of the groupbox to movie it. That or use the Location method which takes a point object.
Hope this helps!