Does Korf actually, or directly challenge Hooks Law?
If his calculator doesn't calculate the same eigenfrequency as the traditonal calculators, then yes.
Do the traditional calculators completely or accurately represent Hooks Law?
If they use the following formula: f=1/(2π√M⋅C), then yes. This is literally Hooke's Law.
All 'traditional' calculators calculate the exact same figure with the same input parameters, so I figure they all use this formula (Hooke's Law)
Furthermore, if he’s “wrong” then why does his calculator work whatever % of application (appears to work more often than not).
What makes you say his calculator works?
Wong number is wrong number.
There ‘s obviously issues with calculators, are these issues (In Vitro vs In Vivo), a misapplication Hooks Law.
Afaik there are no issues with the traditional calculators.
Why do some cartridge/tonearm combo’s work well that are presented as extremely mismatched by calculators?
"Work well" is not an objective statement. The calculators only calculate the eigenfrequency of the resonance (spring mass system)
Whenever someone attaches the label "work well" to it, then it becomes an interpretation, not a hard number. And this is about calculation hard data (it's a calculator), not subjective interpretations. A subjective interpretation is whether or not this all is important in the greater scene of life

Korf’s research and applications also fails to answer the question but it comes closer in some respects, doesn’t it?
No. his calculator gives an incorrect representation. Both in eigenfrequency (at least some examples that I tried, I haven't tried all combinations obviously) as in predicted amplitude of the resonance (I think it's way higher based upon both wave analysis as just watching the resonance).
Your question should be the other way round. Korf asks the right questions, but imho what he comes up with doesn't come closer in many respects.
Like I stated before, imho the only thing his caculator represents correctly is that acceleration of the headshell increases when the resonance frequency becomes higher, given when the amplitude stays the same.
This is only logical, higher frequency means the headshell changes direction more times per second. That automatically means higher acceleration. You don't need a calculator for that.
But why are you such a firm believer in Korf's calculator?
Have you actually measured resonance frequencies in a calculated effective mass arms and known compliances (or measured the same cartridge in different calculated effective mass arms) and put those numbers in both the korf calculator and a traditional calculator and have found the Korf calculator giving the correct number and a traditional calculator an incorrect number?
Or have you measured amplitude of a resulting resonance, cross referenced it with the amplitude when the cartridge is not in resonance and compared that with the 10% or 20% rise in resonance that the korf calculator predicts and found that correct?
If you have documented such measurements I would love to see it, because my findings are different.
If you just look at my video, I see at 11 and 12Hz an amplitude of the resonance that is way more than 10% or 20% of the amplitude at say 7 or 8Hz, where as you can see in the screenshot of the korf calculator that I posted, the excursion of the headshell at the peak of the resonance is well below 12,5mm (that would be half way inbetween the 10mm line and 15mm line) whereas at lower frequencies below the eigenfrequency, the excursion is stated at 10mm.
That difference is just way to low.
Regarding the acceleration of the headshell excursion, what Korf's calculator basically tells you, is to stay below 10,25Hz. Every combination that I tried that falls just in the 'green zone' is calculated at ~10,25Hz. But do you need a separate calculator for that? One sentence that tells you that should be enough I believe?
His examples of what acceleration is good or bad are so extreme (a 5CU denon DL-103 in a 14gr arm for example, or a 40CU cart in a 40(!) gram arm....) that he just plays captain obvious here.