Ada,
I think I agree with your points. The meaning of words/notions like "knowing" and "believing" are not written down in marble anywhere, and throwing dictionary definitions (whether ancient or modern) at each other doesn't make much sense. In the end, every speaker/writer makes its own definitions, which can at least be gathered from their usage if they don't make it explicit; to some faith and knowledge are almost synonymous, to others they are opposed, and still others are inconsistent (nothing wrong with that imo).
As I briefly tried to point out in my last post, "saving faith" in the Synoptic Gospels is remarkably non-dogmatic (contrary to Paul for instance, where it relates almost exclusively to the, or rather his, "Gospel"). There is a recurring paradox: not only monotheistic Jews but the disciples are often described as lacking faith, while total strangers (especially Gentiles, the Syro-Phoenician/Canaanite woman, Roman officials, etc.) are ascribed great faith. There is of course a religious agenda behind (praising mostly Gentile Christianity over Judaism), but also a certain reluctance to enclose faith within too definite borders (otherwise the disciples would be by definition on the "good" side).
That the subjective experience of faith can become a basis for not absolute but solid knowledge, this is beautifully illustrated in the pericope of the blind man in John 9: "If he is a sinner I don't know: I do know one thing, I was blind and now I see."
Gopher
Atheism was not unknown in the Ancient world; we can construe it as implied by several schools of Greek philosophy, e.g. atomism (Democritus, etc.) -- rarely claimed though, because it was a criminal offence in Athenian law, cf. Socrates' trial and condemnation (although Socrates denied being an atheist, by Plato's Apology). However it was relatively rare, especially outside the Greek sphere, and I think the notion of "moral" or "practical" (vs. theoretical) "atheism" applies to Psalm 14 quite fairly. A book like Ecclesiastes takes "God" (or more abstractly "the deity," ha-'elohim) for granted but clearly disconnects him or it (apart from a few likely "pious" additions) from moral judgement and retribution. Interestingly the Sadducees (whose ideology was very close to Ecclesiastes) were often termed "Epicurean" by their Pharisaic-rabbinical adversaries.
Hebrews (which I think is not Pauline by any stretch, in spite of the Pauline-like addition in chapter 13, nor addressed to anyone in Jerusalem -- Rome seems to be a much more likely setting) reflects a very particular philosophical background, obviously influenced by the kind of middle-Platonism which is also evident in Philo of Alexandria. His "definition of faith" should not be extrapolated or absolutised as THE Biblical definition of faith I think.
To the author of Hebrews, faith is a kind of knowledge: knowledge of the invisible/eternal; and (there lies the common misunderstandings); his point is not that faith requires "evidence" of any kind: the very existence of faith and the actions it inspires (which is the point of chapter 11) is elegkhos, demonstration, evidence, warrant, proof, manifestation amongst the visible/temporary world of "shadows" of the very being or essence (hupostasis) of the invisible/eternal. The point of v. 6 in particular makes sense from this perspective (in the order of knowledge rather than in the order of fact according to the classical distinction): because (1) Abel and Henoch pleased to God (by the testimony of Scripture, not only Genesis but texts like Sirach 44:16 or Wisdom 4:10) and (2) without faith nobody can please God (the "logical" argument of v. 6), we know they had faith (which is the evidence for the invisible/eternal).
(I don't mean you or I have to agree with the rhetorics, only pointing out how it works.)
The works (pseudo-)James recommends have nothing to do with ritual (and hereby the pseudepigraphic author certainly departs from the "historical James"): they are consistently and exclusively "humanitarian" if you allow me this anachronistic word (cf. 1:27 and the context) -- a domain in which he finds post-Pauline churches, absorbed in debates around theoretical "faith" they deem saving, sorely lacking.
Hope it helps a little... :)