Are properties such as locality and realism properties of all theories, some theories, or interpretations of theories? I have a strong intuitive feeling, based for example on the Bothe-Geiger experiment, that quantum mechanics is nonlocal. But intelligent people who have thought about these things make claims such as that quantum mechanics is nonlocal in the Copenhagen interpretation, but local in the many-worlds interpretation. It seems clear to me that some theories (Newtonian gravity) are definitely nonlocal, and others are definitely local (classical special relativity).
Here are some of the terms used to talk about the EPR paradox:


*

*locality

*realism

*counter-factual definiteness


Do some or all of these have definite true/false values for quantum mechanics? For certain interpretations of quantum mechanics? For hidden-variable theories? Do certain boolean combinations of these terms have definite truth values, even if the terms themselves do not?
My current feeling is that these are all fundamentally incoherent notions, and that we should understand them as nothing more than vague philosophical motivations that would lead us to construct actual theories such as hidden variable theories, or to construct tests such as the Bell inequalities. Is my opinion sloppy and overly broad?
related: What combinations of realism, non-locality, and contextuality are ruled out in quantum theory?
 A: Starting at your end: Yes, of course we are free to choose whatever notions we like to construct a theory, and then to test its predictions with experiments and iterate the process. 
Locality in the sense of Einstein's special relativity is a well tested concept. There can be no instantaneous information transfer between space separated events as happens in Newton's gravity, which led to the latter being supplanted by GR. 
The standard utilitarian formalism of QM, and more explicitly QFT, is manifestly local. There are no non-local interactions. What we do observe are non-local correlations, which tend to be stronger than non-local correlations in classical physics. This has been demonstrated several times by various loop-hole free tests of Bell's inequalities.
I interpret "realism" as he same as "counter-factual definiteness" in the sense that objects have pre-existing values even before we make measurements to determine those values.  The standard formalism of QM/QFT does not refer to such concepts and attempts to include such possibilities within QM leads to contradictions. 
The conclusion of Bell type experiments is that theories with "local realism" do not agree with experimental results, while QM predictions agree perfectly with those experiments. So if you keep locality, then you have to give up realism, and QM is the best theory in this category so far.
But if you insist on keeping realism then you are forced to adopt non-locality. Here the debroglie-Bohm theory, which is just a re-writing of standard QM, is a concrete possibility. However such a formulation is currently known only at the non-relativistic level. 
