Brocolli, I would like to continue the discussion on the title since I can not chat simultaneously. If this "discussion" is not appropriate here, please delete.
Anyway, I found out I must drop my case for "a certain case".
Since the researcher studying about なかで、and うちで, so on, and on, she specifically says she is studying the case with the particle with なか、うち、I have to conclude according to the professor, なか, うち as nouns.
However, I found out some exceptions.
Example, 殊の他、meaning especially, would be categorized as an "adverbial clause(sentence)"
But quite limited and other is such as 真、あっぱれ, meaning GJ! General! but this is too old fashioned. And others, as you said, ex こんな環境の中(なか（oops!))、こんな事出来ません。 meaning, ”Under these kind of circumstances, we can not do this!".
What is your opinion about this? I only found at any case, comma is needed. ( may be this comma is swappable with the particle )
Any sourcce will be welcome.
Thanks.