version 1.6.062 i think...
The Extension Manager is basically used to unzip any .mxi files you may download of the web. mxi files are packages that contain an extension to Flash- such as a command, component, tool, or effect- and an xml file containing to any information about these extensions... like descriptions, what directories to place them, etc.
You mainly use it when you double click on an mxi file you have downloaded, but you can always open the extensions manager and check out which extensions you have from outside sources and their info. You can also send any extensions you have made or visit the Macromedia Exchange site from the File menu
As far as the Flash Project... i'm not sure. don't use it. But i assume it's an easy way to navegate to and associate flas, jsfl, classes pertaining to a project from within flash, instead of having to go to File>Open to find any files pertaining to a project- kind of like Dreamweaver's Sites panel.
hope it sheds some light.