As part of developing scripts and to save the other services/resources accessed by ArcGIS, is there a way or separate installer to install Python and ArcPy libraries alone without installing ArcMap?
Arcpy must be installed with one of Esri's applications like ArcGIS Desktop, Arcgis Server, ArcEngine. With Arcpy, there are dependencies on arcgis binaries (dlls).
You can install just ArcPy by installing ArcEngine, but this comes with all of the libraries and dependencies that come with Engine. The luxury of this is that Engine is cheaper to install and it can also be run on Linux.