I was writing a comment on the "one and the same" idiom but the page was deleted before I could publish it. So here are my thoughts:
I do think it's an idiom since it's not a combination of words you'd randomly choose, but it's rather an established expression. Linguistically speaking, "one and the same" is a tautology, i. e. it "says the same thing twice". There are certain established tautologies (such as "forever and for all" and "one and only"). Someone who is not familiar with the respective expression might need an explanation that it's an intended redundancy not for the sake of creating a distinctive "ad-hoc" stylistic effect but simply because it's commonly said. So overall, I think "one and the same" does qualify as an idiom.