You can try to use a symbolic link to use the engine from another location, here is an example for UE4.11 (works with any other version too):
- Copy the 4.11 folder from C:\Program Files\Epic Games to your destination location.
- Delete the 4.11 folder from C:\Program Files\Epic Games.
- Open cmd and navigate to C:\Program Files\Epic Games (cd C:\Program Files\Epic Games or SHIFT + Right-click inside windows Explorer in the folder and click “Open CMD here”)
- Enter this command: mklink /j 4.11 D:\MyUnrealEngineStuff\4.11 (Replace the second path with your destination location)
About projects, you can move them to any location since the Launcher should detect projects at other locations too (if not, just start the editor using the *.uproject file once)