I would like to know which version of ArcGIS/ArcMap I need so that I can install the HEC-GeoHMS extension..? Is the latest version of ArcMap 10.8 applicable or do I need earlier versions..?
I think you should be able to get the HEC-GeoHMS extension for 10.8 at the link below. Extensions are available for earlier versions of ArcGIS for Desktop.
v10.8: https://downloads.esri.com/archydro/HECGeoHMS/Setup10_8/
Other versions of Desktop: https://downloads.esri.com/archydro/HECGeoHMS/
The most stable one I've used so far is ArcMap 10.2, and i think it is the last officially supported one.