A summary explaining those ancient Indian philosophies of those non-Buddhist schools that had debated with Buddhist, especially Nalanda, masters? Can anyone share or tell: where can I find a summary explaining those ancient Indian philosophies of those non-Buddhist schools that had debated with Buddhist, especially Nalanda, masters? For example, those philosophies of those opponents in Indian Buddhism Śāstras (i.e. treaties).
I ask because I am studying some texts on and also pondering on the tenets system/theory of Indian Buddhism, and I would like to be rigorous in understanding what non-Buddhist philosophies are refuted grounding in reasoning by Indian Buddhism (Nalanda) masters.
You might be looking for a scholarly paper which lists the non-Buddhist schools and their philosophies (for which I don't have an answer).
The sutta which comes to mind as likely relevant to your question is Brahmajāla Sutta (DN 1) -- which I think lists sixty or so wrong or non-Buddhist views.
Piya Tan as a more detailed (highly referenced) translation and commentary of this sutta (and of many other suttas too). The URLs on his site aren't quite stable but they're currently:

Brahma,jāla Sutta -- The Discourse on the Perfect Net -- D 1
A Commentarial Guide to the Brahma,jāla Sutta