Can I move applications downloaded from the App Store? I have way too many applications and sadly sometimes I forget if I have an application for a particular purpose.  So I thought I would like to organize /Applications into folders.  For example "Audio, Video, Development, Design, etc."

What will happen when an application updates from the app store?  Will it update the version that is in the folder or will it be downloaded to its original location in "/Applications"?
Yes, you can move the applications. Providing the destination remains in the Spotlight index, the Mac App Store will continue to update the app.