Word Usage – When Are ‘If’ and ‘When’ Interchangeable?

This sense of can is what linguists call a negative polarity item (NPI). You're already aware that can't can be used to mean "is not possible", and you clearly have little difficulty accepting that can can be used to mean "is possible" when the context effectively negates it ("I don't think that …"). So the tricky part is just recognizing that in English, negative polarity items are also licensed by (i.e., allowed to occur in the context of) questions.

Another negative polarity item is any; as you can see from these examples, they have similar distributions:

• Direct negation:
  • 1 isn't greater than any other positive integers.
  • 2 can't be greater than 3.
• Negation in a matrix (containing) clause:
  • I don't think 1 is greater than any other positive integers.
  • I don't think that 2 can be greater than 3.
• A question:
  • Is 1 greater than any other positive integers?
  • Can 2 be greater than 3?
• Use after only:
  • Only 1 is greater than any other positive integers. [This is false, of course, but the statement is grammatical.]
  • Only 2 can be greater than 3. [Ditto.]

Note that not all NPIs are licensed by the exact same contexts: some require more thoroughly negative contexts than others. Also, a word can be an NPI in one dialect, or in one register, without being an NPI in a different dialect or register. So this is a rough observation, rather than an firm guarantee of identical behavior. But it's a good first approximation.

A search term is 'proper postpositive'. This has been discussed in other answers:

proper -- can this postpositive adjective be substituted for "in and of itself"?

https://english.stackexchange.com/questions/354077/use-of-proper-as-a-postpositive-adjective

From wiktionary:

(usually postpositive) In the strict sense; within the strict definition or core (of a specified place, taxonomic order, idea, etc).

Which matches the Cambridge definition you mentioned:

"belonging to the main, most important, or typical part"

It's the "core" part of something. The object in the strictest sense of the word.

The word "itself" is more general, and can be applied in multiple ways, but the main sense here is "The object, the thing, 'by itself', separately, and not dependent on other things."

"Itself" is closely related to "himself", which could be used in an example:

He finished the repairs (by) himself.

That is, without assistance.

If A and B are clearly different things (already), and we say A itself (without B) , that means A separately from B, and without dependence on B.

Going back to "proper", that's referring to the "core" essence of something. The real city, and not the suburbs.

There is similarity between "proper" and "itself". The word "itself" is used to point out a separation and a difference between two things. X and not Y. But usually in the case where X and Y aren't being confused with each other. "Proper" is used to distinguish between the "core main" part, and the "extraneous extra" parts, and when perhaps those two things were confused with each other.