Updating / Upgrading Xcode to 6.0.1 does not work so I tried to upgrade my Xcode to 6.0.1 from 5.6 or something. I'm running on Mac OS X Mavericks 10.9.5 yet. 

The problem is that it starts downloading Xcode form the Mac AppStore and already 
replaced my old Xcode. So in the dock it is shown like a normal icon and when I click on it it says 

"Xcode is being updated. Xcode can not be launched while updating"

When I open the AppStore it restarts the update and so on. So what I did was to download Xcode from the Developer's Resources site. Then I opened the .dmg and it gave me the image like opening a CD (I don't know how to call it, sorry). Then I copy the program to the desktop and it starts copying (preparing to copy) and nothing happens...

Then I tried to open it directly from the opened .dmg but just literally nothing happens...

Also I tried to deinstall "Xcode 6" with CleanMyMac2 but it starts deinstalling and says it finished right a second after.

Sorry for the long text but I thought an exact description might help you. Thanks for taking your time reading this, i'd appreciate an answer if you have one ;)
Try deleting the Xcode.app from your /Applications folder and replacing it with the Xcode.app from inside the dmg that you downloaded. Once you have replaced the Xcode application try to open it and it should work. You usually can't run packages or applications from inside of a mounted dmg. It is recommended to copy what you need from the dmg and then running it.