“Research into” suggests you’re researching information that is already out there—reading published studies, watching news reports, combing through websites, etc.
“Research on” suggests you are conducting primary research to find new information—interviewing people, science experiments, quantitative/qualitative analysis, etc.
Examples:
“My research into the university’s recent news highlights its extensive community outreach”
Research “on” wrongly hits the ear here because it can sound like you’re stupidly attempting to say you put together this news yourself, when the sentence makes it clear you did not.
“My research on the reception of the university’s recent PR campaign suggests it is working”
This sentence tells the reader that you are talking to the university’s audiences yourself and analyzing responses to form a conclusion.
There are probably certain sentences where you can use “research into” and “research on” interchangeably, but keeping the above shortcuts in mind can help eliminate ambiguity.
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.
Best Answer
They mean the same thing but are used in different contexts.
deem is used in contracts and legal language (legal briefs, etc.) and is generally used in written texts. It is not used verbally as much as it is very formal.
consider is used everywhere: in speech and in writing.
That is the only difference I know.