Is it possible to filter RediSearch’s GEO field by an axis-aligned rectangle instead of radius?

The GEOFILTER command (and query syntax for geofiltering) only have a radius parameter.

Since the GEOSEARCH command has BYBOX option, is it possible to use GEOSEARCH command on the geospatial index created by RediSearch module?
(What is the key name of auto generated spatial index, if for example, we have RediSearch’s index named “myIdx” and GEO field named “location”?)

No. RediSearch supports solely radius search.