I think that those are perfectly reasonable questions. It's not something that you think about a lot as a lawyer - at least not explicitly - because you get so used to this pattern.
Thinking about it, it might be easier to explain this by taking the two steps in the opposite order.
I don't agree that reasonableness is the bane of all our laws. It's an important safeguard - the point is that we are dealing with subjective judgments or subjective feelings, but we want a safeguard so that someone can't be liable because someone completely overreacted to an innocent remark, or a police officer completely overreacted to very minor evidence.
The question that this is asking is "could a reasonable person, in the position of the victim, have been put in sustained fear" (or in your police example, could a reasonable police officer put in the position of the officer in question have suspected X). The reasonable person is assumed to be of reasonable firmness and resolve, to take sensible logical decisions etc. Note that the question is could a reasonable person, not would they - the person does not have to act in the way that the court thinks a reasonable person would probably act, they just have to act in a way that falls within the spectrum of actions that the reasonable person might take.
In practice, where the person is an expert the court will be slow to find that they have acted unreasonably, especially if they act within the bounds of normal practice in their profession. In principle I think that is sensible - the court is meant to check excesses, not ensure that every officer meets absolute best practice. However it does seem like the pendulum has swung too far at present, particularly in the United States, and I wonder if the fact that US judges are highly politicized means that you are likely to get judges who are more likely to side with the police (I don't mean that they are being swayed by thoughts of rewards for siding with the police, just that the executive is likely to appoint judges who they know take a more pro-executive view).
The subjective limb
This is a straightforward evidential point - straightforward conceptually, that is, not necessarily easy to prove. Subject to the applicable rules of evidence, anything that is relevant can be used to prove that the person was fearful - I'm not aware of CAT scans having been used, but expert evidence from psychiatrists, therapists, police support officers and so on are all used.
Proving that someone was fearful is obviously difficult since it requires the court to try to establish what was in their mind. There are three points though that I think tend to mitigate that problem:
1. This is not an isolated difficulty - the courts are frequently required to establish what was in someone's mind (did she intend to stab him?) and have a lot of practice at it.
2. The criminal standard of proof applies - so the prosecution has to establish beyond reasonable doubt that the person was fearful.
3. They aren't looking at this as an isolated question - they can look at all the circumstances. If, in answer to the other limb of the test, the court has concluded that the defendant's behaviour would have put a reasonable person in sustained fear, they are going to find it rather easier to conclude that this victim was, in fact, in sustained fear. For example, if you make repeated and plausible death threats that the court thinks would have terrorized a reasonable person, and the victim claims that he was left fearful by them, you are likely to find that the court is not very receptive to the argument that the victim is faking it.
As a final point, I don't think it can all be quantified objectively. That, however, is true of an awful lot of criminal laws, even the seemingly straightforward ones. My view is that it's an inevitable product of the fact that we live in a confusing and complicated world.