Do most native English speakers recognize two (or more) meanings for "itemize"? Is one meaning dominant and the other(s) rare? What about non-native speakers?
At least here in the U.S., I think most speakers would recognize a sense — call it 'sense A' — whereby the direct object is a singular noun denoting a totality that can be broken down into items, as when we itemize a list or a receipt (or, obviously, a plural noun denoting multiple such totalities).
I also think most U.S. speakers would recognize a sense — call it 'sense B' — whereby the direct object is a plural noun denoting such a totality, as when we itemize our expenses or our tax deductions — not necessarily because this is a distinct sense, but simply because it's perfectly natural in English to use a plural noun to refer to a single totality. (For example, "he shared his M&Ms with her" does not mean that they shared each individual M&M!)
Some U.S. speakers would also recognize a sense — call it 'sense C' — whereby the direct object is a singular noun denoting an item resulting from breaking down such a totality (or, obviously, a plural noun denoting multiple such items), as when we itemize a certain tax deduction. I think this sense originated as a backformation from the second sense; speakers who have this sense would probably be surprised that I felt the need to distinguish it from that one. But personally, I find this sense rather awkward, and Google searches suggest that it's quite rare compared to the others.
Do you think I'm right about the meaning of the second dictionary.com definition? If not, what is the meaning of the second definition?
That definition sounds like it's trying to define sense C, but since sense C seems to be quite rare, and the example sentence works perfectly for sense B, my best guess is that it's trying to define sense B in a way that also works for sense C.
In either case, I don't think it covers the usage you give as your motivation, since that usage does not involve breaking down a totality.
Are there yet more definitions of "itemize" beyond the two that dictionary.com lists?
Well, you've given a usage that's apparently a different sense: "itemize" meaning "create an 'item' from". :-)
Am I right that the meaning of dictionary.com's second definition emerged from usage of "itemize" in instructions on US (or UK?) tax forms?
If their definition refers to my sense B, then I doubt it.
If it refers to sense C, then I don't know, but it would certainly make sense: "itemize" is accounting jargon, and tax forms are most Americans' greatest source of exposure to accounting jargon. It's very common, in all fields, for non-specialists to adopt jargon and use it in related ways that specialists might feel strange about.
Does the second definition always imply that the first definition also applies to the composite object, just elsewhere than the immediate listing context?
I'm sorry, I don't understand this question.
[…] what do you think that better single word might best be: ¶ […]
This question is probably too subjective for this site, but personally I think any of your suggestions would be fine. Another option is to introduce a hyphen ("item-ize").
Best Answer
Frame of reference
With respect to the first example sentence given ("his own cultural frame of reference"), this is related to moral or cultural relativism/absolutism.
In the second mathematical definition it means that measurements can be taken from different points of reference, for example, absolute and relative coordinates. If you have a square on a screen it may begin at coordinates (200, 200), but another square inside that square might have absolute coordinates of (300, 300) but relative coordinates of (100, 100), relative to its parent square.