First I installed/uninstalled several times ArcGIS Desktop 10.2.2 +BG64 and each time it led to issues with the python shell, in particular I was unable to run python and I realised it was due to innapropriate python27.dll files (32 insetad of 64 version in win32). Each time I carrefully removed everything from ESRI/ARCGIS/PYTHON and only reinstalled from the esri.exe.
Now I decided to go back to 10.2 (the version I previously had) and again installed Desktop + BG64. Now I can open the python shell (64) and use it for basic things but when importing arcpy it crashes. The 32 shell does not crash. I checked the dll with dependency walker. I checked the InstallPath and PythonPath in the register.
After several installing/unistalling and still having something which is not working I do not know what to do...