Is ArcMap 10.7.1 a 32- or 64-bit application?
I´m familiar with 64-bit ArcGIS Pro, but what about ArcMap?
Yes, ArcMap, ArcCatalog, and the other UI tools of ArcGIS Desktop (except Pro) are still 32-bit at 10.7.x. They will also be 32-bit at 10.8.x.
Both 32-bit and 64-bit versions of ArcPy exist for Python 2.7 (the latter in the optional 64-bit Background Geoprocessing in Desktop). ArcGIS Server has been exclusively 64-bit since 10.1 (also Python 2.7).
64-bit ArcPy is available with ArcGIS Pro for Python 3.x, and the ArcGIS API for Python is also Python 3.x.