The tag of common-law in your question and your wording about "applying subsequent legal principles" make me wonder whether the scope of your inquiry is limited to precedential decisions issued by the judiciary. It is otherwise unclear which scope you have in mind for this question.
It is very difficult (if at all possible) to identify case law that does not purport itself to be premised on legislation or deeply rooted doctrines such as contract law. But if your inquiry is broader than purely common-law and stare decisis, the following may clarify.
What's the difference between “a question of fact” and “a question of
Questions of fact seek to ascertain what happened, or whether a specific event or circumstances meet the statutory requirements or, accordingly, the prima facie elements of the type of claims at issue. By contrast, with questions of law, the inquiry is: "what remedies/sanctions/implications (if any) does the law provide for that class of wrongs?".
A real-life example illustrates the difference:
During a court hearing in year 2015, Michigan judge Lisa Gorcyca bullied, extorted, terrified, and for 17 days jailed three innocent kids simply because they refused to have lunch with their father.
That deplorable mess raises questions of fact such as:
- Did judge Gorcyca belittle, threaten, and yell at the Tsimhoni siblings?
- Did she order one or more of them handcuffed as per their refusal to
have lunch with their father?
- Were one or more of these kids jailed for 17 days?
- Did judge Gorcyca cause all this at a court hearing she presided?
By contrast, questions of law guide or dictate how a situation of that type is to be remedied. For instance, the actionability of "maliciously proceeding against someone" (in the vein of what the Tsimhoni kids endured) is a matter of law. See MCL 600.2907:
Every person who shall, for vexation and trouble or maliciously, cause or procure any other to be arrested, attached, or in any way
proceeded against, by any process or civil or criminal action [...]
shall be deemed guilty of a misdemeanor, punishable on conviction by
imprisonment in the county jail for a term not exceeding 6 months.
Likewise, see MCL 750.213:
Any person who shall [...] orally or by any written or printed communication maliciously threaten any injury to the person [...] with
intent to compel the person so threatened to do or refrain from doing
any act against his will, shall be guilty of a felony, punishable
by imprisonment in the state prison not more than 20 years or by a
fine of not more than 10,000 dollars.
(Note that the legal definition of injury states in relevant parts "[i]njuries to those rights which a person possesses as being a member of society", and "[a]n infringement or privation of the civil rights which belong to individuals", Black's Law Dictionary. Thus, injury to the person is not limited to physical violence.)
But another question of law precludes actionability against judge Gorcyca: The question of whether a judge's acts of brutality performed in her official capacity are protected by judicial immunity. This question is always answered in the affirmative. In other words, it is an absolute privilege.
Thus, as a[n outrageous] matter of law, judge Gorcyca's brutality is protected by judicial immunity despite the vast, unquestionable evidence of what she openly did to these three kids as a judge.
Another frequent and rather trivial example of the difference between question of fact and of law is the statute of limitations. In this type of scenarios, the question of law is "what is the statute of limitations for claims of the type XYZ?", whereas the question of fact would be "when did the plaintiff file the pleadings pursuant to his claim of XYZ?".
Are they indeed indistinguishable, such that appellate judges are free
to twist the definitions whichever way they prefer for any given case
(as was suggested in 1 of the legal reform articles that I read)?
No. They are not indistinguishable. In theory, appellate judges are not free to twist the definitions. And while I cannot think right now of an instance where they twist the distinction between question of fact and of law, I know by personal experience that judges (at all levels) wantonly distort the facts of a case so that they can force an outcome which is contrary to the evidenced truth. For details on these specific cases, see my briefs here, here, with evidence & court records I have been posting (as time permits) on various pages of my site as well as on Youtube.