tl;dr: Your points 1 to 5 are misunderstandings. The answer to your question follows from a better understanding: Entanglement is no active link, hence there is no need for instantaneous action. However, if you want a certain kind of ontology, then you must accept a certain kind of instantaneous action/non-locality (which doesn't necessarily violate information causality).
Disclaimer: I'm neither and expert in philosophy nor in what people think. So if anybody finds faults in my descriptions, please do correct them.
- Entangled particles were found to have opposite spin in each and every angle. This has been demonstrated experimentally without any doubt. And this observation required "instantaneous action at a distance".
This is both historically and factually wrong. Entanglement is defined as "not separable", where separable has a precise mathematical definition as being a convex combination of product states (see here). In an experiment, this can be seen in many different ways - especially since entanglement can exist between arbitrary many parties. A special scenario is the case of two people sharing a maximally entangled state that is perfectly correlated. This is the scenario you describe which can be produced and tested experimentally.
An observation as such doesn't "require" anything only an intepretation does. However, when people discovered entangled state (i.e. EPR), it seemed to them that it does indeed require instantaneous action at a distance because they were making other implicit assumptions about what should be the case. This is what Einstein described to Bohr in some of their letters and what he didn't like at all (according to Wikipedia, you can read about it in the book Albert Einstein, Max Born: Briefwechsel 1916–1955).
Let me stress already at this point that today we understand entanglement as nonclassical form of correlation which does not in any way need action at a distance.
- Einstein (or EPR) suggested no need for "instantaneous action at a distance", the behavior can be due to hidden variables.
No, this is not what the paper suggested at all. The paper is concerned with the question of whether the wave function is "real" and in particular the reality of the wave function. The question is the following: If we think that the wave function is the "real thing" and describes complete reality, then this should mean (definition in the paper) that for every measurable quantity we should be able to predict its outcome definitely if we know the wave function.
The paper shows that this is not possible with entangled states. There are (at least) two ways to interpret this: One can say that this reality as Einstein wants it doesn't exist or that the wave function is just not the full description of reality. If you endorse the latter, the next question is what the full reality is and whether you can know it (philosophically, this is the difference of epistemology and ontology).
Einstein deeply believed that there is an underlying reality (ontology) and therefore he needed hidden variable models. However, the paper clearly states that the authors do not possess such a hidden variable model at the time.
Let me quote:
While we have thus shown that the wave function does not
provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible.
In other words, what Einstein felt is: We need another theory "hidden variables" because quantum theory is not complete. The wave function is not what we are after.
- People kind of agreed with EPR till Bell came up with Inequality.
Not really and I strongly suspect that most people just didn't care. The physics was universally agreed upon but the equipment could not test it yet. The phenomenon was only tested in the lab in the late seventies and the paper has slumbered for decades. Also, the underlying questions people might differ upon (as pointed out above) are philosophical and were not accessible to experiments, so people just waited. Most others who cared went with Bohr and just held the view that such a realistic description was not possible. Some, such as Bohm tried to vindicate Einstein's views and suggest a completely deterministic hidden variable theory (see Bohmian mechanics).
- People have been citing Bell's Inequality to disprove "Hidden Information Approach" and been claiming therefore "instantaneous action at a distance" is real. (Well, if you ignore the loopholes, which is ok)
Once again: No. One of the main problems is that you confuse two concepts: hidden variables and local hidden variables. The distinction is extremely important.
Essentially, Bell made the following two assumptions:
- We want a theory that is "real" in approximately the sense that Einstein wanted (I paraphrased above).
- We want a theory that is also "local" in that causes must propagate with a certain speed and cannot be instantaneous.
People (especially Einstein) want the first, because it is ontologically nice and people want the second, because it seems to be required by relativity and our knowledge of how the world works.
What Bell did was to device an experiment that could prove that one of the two assumptions must be wrong (ignoring loopholes). A (deterministic) hidden variable (information) theory would be a theory of the first kind and therefore what Bell claims is that you can make an experiment that would show that the world cannot be described by a local hidden variable theory.
What does this say and what not (also see the abstract of the original paper)?
- It does not say that hidden variable theories are impossible - indeed Bohmian mechanics provides such a concept, although they have troubles incorporating relativity.
- It does say that any such theory must be nonlocal (as indeed Bohmian mechanics is).
- It says that we cannot have a theory such as classical mechanics for quantum mechanics.
What does locality say? How does it connect to "spooky action"? People have understood nowadays that a nonlocal theory might not necessarily violate observed causality in that we might never be able to devise an experiment that violates causality although the theory is nonlocal. This is possible if we cannot achieve perfect knowledge of the universe and boils (once again) down to a philosophical difference of ontology versus epistemology.
- Bell's Inequality supports/proves "instantaneous action at a distance" based upon a statistical correlation between spins of entangled particles at different angles.
No, see above. Also let me stress once again: You can in no way use that experiment to transmit information faster than light and this was not suggested by Bell. As far as I know, Bell was against nonlocality and favoured a nonrealist interpretation of his result, but this is completely irrelevant.
This should also render your specific question: If you want realism, Bell tells you that you have to have some form of locality. However, subsequent analysis of the experiment shows that you cannot use the nonlocality to violate causality or in other words: Bell's experiment cannot decide which of the two scenarios (nonlocal hidden variable theory OR local theory without ontological realism) is the "correct" one or whether this question even makes sense.
So what's the physics in all of this? Entanglement is correlations. We cannot use the correlations to send information faster than light, thus we don't violate this part of causality. We can use the correlations to do a whole host of other things like quantum teleportation or maybe one day even quantum computation. This is experiments, so it's physics.
Also, Bell's theorem tells us that naive classical approaches to devise a theory for this behaviour must fail. Since quantum theory works extremely well, most working theoreticians don't have to be overly concerned by this fact and so most theoretical physicists don't care. There is also the very real possibility that the two different options of Bell's theorem (if the loophole-free tests are really loophole-free) will not lead to any new physical predictions. There might be deep physics hidden that many years of trials have not revealed, but there might just as well be no physics other than the first sentence of this paragraph.
The rest is metaphysics and philosophy. Whether or not you fancy a nonlocal or a nonrealist approach is for you to decide (or not care at all since it's not physics). Maybe one day somebody actually comes up with an experiment to distinguish the two, but until then you may as well get back to doing other experiments and describing them.
