It has been a while since I mixed versions of Esri software on the same machine. I recall it technically working, but I also believe Esri would recommend not doing it.
Regarding Python, ArcGIS for Desktop and ArcGIS for Server each have their own, separate Python installations. Since ArcGIS for Desktop is a 32-bit application and ArcGIS for Server is a 64-bit application, the former has a 32-bit Python installation while the latter has a 64-bit Python installation. When using the same version of software, there is a potential overlap in Python installations when 64-bit Background Geoprocessing is installed for ArcGIS for Desktop because it uses a 64-bit Python installation as well. In this case with different versions of software, the Python installation versions will be different as well.
From a Python perspective, you will have 2 or 3 separate installations depending on whether you installing 64-bit Background Geoprocessing. The Python installations are mostly self-contained, so having multiple ones shouldn't affect any given one from working. That said, Windows can only do Python file-type associations for a single Python installation, so you will have to be careful about which Python installation is being used when running a Python script using default file-type association. Also, make sure you are aware of what Python installation your Python IDEs are pointing to since you have multiple ones on the same machine.
