Where on the OSX Mavericks is the Applications folder supposed to be?
There is absolutely nothing wrong. That is how your Apple is suppose to be. /Applications , /Library , and /System are managed and used primarily by the OS. Your files should be in your user folder /Users/john for example. If you want you can create another folder in your home folder (user folder) called Applications or Programs or "whatever" and put third party apps in there. It is your choice but you shouldn't remove any applications from the /Application folder should they automatically be installed there or be default programs, doing so will result in issues.