If you hit axis key (x,y,z) once it will assume Global; if twice (xx, yy, zz) this will be the orientation currently chosen in the dropdown (Normal, Custom…). 3d cursor will be the symmetry point, half the distance on a chosen axis, if pivot is set to it.
To have something attached to the faces (e.g we want a monkey on each of the Icosphere’s faces) use Duplication (on Object tab, a bit down); can be set to verts, faces, frames (which is interesting but i personally try to avoid it) and group which is the same as if you had opted for group instancing from Add menu i think, not quite sure.
Process for the Vert and Face is - set Duplication on parent object, select obj you want to duplicate, Shift select parent and P to Parent duplicates. The deal is, while object you use to instantiate other objects (parent) is seen in Object mode, in render it is hidden - you have to use duplicated ‘dummy’ (can be some selected and copied to another object vertices, faces only) if you want original to be rendered.
Downside - you’ll be breaking you kbd in 15 minutes if there is more than one level of nesting and/or some origins are off or objects involved have unapplied rotations, scales. For a quick one level it’s easy and fine tho. Objects origin,scale and rotations matter, ofc. Guess there was a monetized addon for this which brings some humanity to all above mentioned.
For 1d_inc tools there’s an official thread in Released Scripts.