I try to understand "Quantum Physics"

Yes, I put "quantum physics" in quotes. Because (I think!) the term is partly used as a label for things that should not be called "quantum physics" at all. Such as physical science that just happens to be about very small systems (systems the size of a few atoms, or smaller).
== The label "quantum mechanics/physics" ==
I suspect one of the many sources of confusion about "quantum physics" could be the way the term might make people think it's one "thing", when really it's many things, some of which don't even fit the label.
=== What the label should mean: ===
Obviously, physics (or "mechanics") that in fact has quantized, not continuous, values. Different examples of such physics don't even need to be related to each other! If they pass this criteria, then the label fits. If they don't, then the label does not fit.
=== What the label also seems to be used for: ===
Physical science that just happens to be about very small systems (systems the size of a few atoms, or smaller). Some of these might not pass the above criteria, and so the label "quantum physics" might not really fit.
== The physics ==
So, what's the physics?  At this point, since the feild of study is still so perplexing and conclusions are so uncertain, it actually might be best to simply list the scientific experiments themselves.  But for now, I'll just list the explanations/conclusions based on the experimental and theoretical foundations.
Accurately labelled "quantum physics/mechanics":
*quantized energy
*quantized particles (matter, light, etc.)
Seemingly random stuff that is innaccurately labelled "quantum physics/mechanics":
*wave-particle duality
*uncertainty principles
*entanglement/coherence
*superposition
*probabilistic behavior
*"information"?
*measured values being caused by the method of measurement
I'll have to check more stuff, such as the Schrödinger equation, to see if there is any relation between all these seemingly random things.  And then, still, if the label "quantum mechanics" will actually be accurate for all of these things.
Here's a great video that gives a visualizatin of the Schrödinger equation, and its behavior.
==What's so puzzling or "strange"?==
So-called "quantum mechanics" is infamously difficult to understand (as reported in the famous Richard Feynman quote), and scientists themselves are divided about interpretations (see Sean Carrol's stuff about "the most embarassing graph").
So what are all those difficulties about?
===Exploration of some articles that discuss this===
In order to discover what the fuss is all about, I'll look at some articles that discuss the fuss.
Sean Carroll's recent "Addressing the quantum measurement problem" seems to give a pretty good summary (at least of the "measurement problem"):
* What precisely happens when a quantum measurement is performed? That’s the quantum measurement problem, in broad strokes
** What exactly is a “measurement”? What kind of system is allowed to make a measurement, and when precisely does it happen? Are measuring apparatuses and observers themselves quantum systems? Do measurements reveal a pre-existing reality, or bring the world into existence?
Sean Carroll's 2005 blog post No reasonable definition of reality could be expected to permit this:
* What we don’t understand is what that word “observing” really means. What happens when we observe something? 
This article, "The Defeat of Reason", really reminds me of my suspicions that a lot of the nonsense and confusion in this topic was sown near the beginning by people with very poor philosophies:
* "So Einstein and Bohr were polar opposites in their approach to physics. Einstein demanded a clear and comprehensible account of what is going on in the physical world—at all scales—in space and time. Bohr thought that the key to quantum mechanics was the realization that no such thing could be had."
* "Bohr took an unexpected approach to this question: instead of asking if the theory was too young to be fully understood, he declared that the theory was complete; you cannot visualize what the electron is doing because the microworld of the electron is not, in principle, visualizable"
* "But in 1926 Erwin Schrödinger produced a mathematically different theory, wave mechanics. Schrödinger’s mathematics was essentially just the classical mathematics of waves.[...] And waves may not be particles, but they are certainly visualizable objects from everyday life."
* "This, in a nutshell, is the central conundrum of quantum mechanics: how does the mathematical formalism used to represent a quantum system make contact with the world as given in experience? This is commonly called the measurement problem, although the name is misleading. It might better be called the where-in-the-theory-is-the-world-we-live-in problem."
* "For Bohr and Heisenberg, the measurement problem is how the unvisualizable can influence the observable (and hence visualizable). For Schrödinger it is how waves can constitute solid objects such as cats."
* "We are left with the question: under what conditions does such an interaction (a measurement of the quantum state) occur? Do we need a human observer? Some conscious detection device, even if not human? Will a mouse do? Some detection device, even if not conscious? The Copenhagen interpretation never answered."
* "for wave mechanics, the measurement problem becomes: When and how does the wavefunction collapse? And the tentative answer is, upon measurement."
* "Einstein was not centrally bothered by the indeterminism of quantum mechanics. What vexed him—as he said repeatedly—was the nonlocality, or, in his pungent phrase, the spooky action at a distance"
* "Einstein saw that the phenomena themselves—as distinct from Schrödinger’s theory with its wavefunctions—did not require anything spooky. All you had to believe is that the electron was always in some precise location, of which we are ignorant, and takes a humdrum path from the source to the screen, causing a flash. But because quantum mechanics does not specify the location, accepting this picture demands rejecting the completeness of quantum mechanics. [...] Bohr never came to grips with this argument. Indeed, it is unclear whether he ever understood it."
* 
From The Trouble with Quantum Mechanics by Steven Weinberg:
*scientists thoguht there were two distinct physical categories, "particles" and "fields".  Light was a wave in the electromagnetic field, electrons were particles.  But then due to experiments, it appeared that light also behaved like a particle sometimes, and electrons also behaved like waves sometimes.
*the electron waves were not made out of matter (like ocean waves are made out of water particles) instead the waves were supposedly "waves of probability".  A travelling electron "is more likely to go in a direction where the wave is more intense, but any direction is possible."
*these probabilities supposedly were not due to unknown information.  There seemed to be a lack of determinism in the new found laws of physice themselves.
*"It is a bad sign that those physicists today who are most comfortable with quantum mechanics do not agree with one another about what it all means. The dispute arises chiefly regarding the nature of measurement in quantum mechanics."
*"the trouble with quantum mechanics is not that it involves probabilities. We can live with that. The trouble is that in quantum mechanics the way that wave functions change with time is governed by an equation, the Schrödinger equation, that does not involve probabilities. It is just as deterministic as Newton’s equations of motion and gravitation. That is, given the wave function at any moment, the Schrödinger equation will tell you precisely what the wave function will be at any future time. There is not even the possibility of chaos, the extreme sensitivity to initial conditions that is possible in Newtonian mechanics. So if we regard the whole process of measurement as being governed by the equations of quantum mechanics, and these equations are perfectly deterministic, how do probabilities get into quantum mechanics?"
*"According to Bohr, in a measurement the state of a system such as a spin collapses to one result or another in a way that cannot itself be described by quantum mechanics, and is truly unpredictable. This answer is now widely felt to be unacceptable. There seems no way to locate the boundary between the realms in which, according to Bohr, quantum mechanics does or does not apply." [this links the issue of "probabilities" with the issue of "we detect electrons as particles, even though they travel as waves", because where we detect the electron is due to the probability, the "probability wave"]
*"in the realist approach, to evolve deterministically, as dictated by the Schrödinger equation; but in consequence of their interaction during the measurement, the wave function becomes a superposition of two terms, in one of which the electron spin is positive and everyone in the world who looks into it thinks it is positive, and in the other the spin is negative and everyone thinks it is negative."
*"nonlocal entanglement" seems weird, for whatever reason
From the page titled "Interpretations of Quantum Mechanics" on the Internet Encyclopedia of Philosophy:
*treating electrons as a wave, calculations of electron trajectories are "successful" (I think this means they predict the diffraction pattern etc?), yet we still seem to detect a "particle" not a "wave" at the end of the trajectory.
*in some calculation or equation (which one?  They don't say) "it looks as if the system exists in several incompatible physical states at once. And yet when the physicist makes a measurement on the system, only one of these incompatible states is manifest in the result of the measurement. What makes this especially puzzling is that there is nothing in the physical nature of a measurement that could privilege one of the terms over the others"
I'd also add one item they didn't acknowledge as incomprehensible (in section 1, where I read so far):
*The wave function seems to predict the probability of finding a particle at a certain location.  How does this probability arise?  Why that probability and not some other?  What causes it?
Here's another article where people try to solve the issues by using a "pilot wave" model:
*"The orthodox view of quantum mechanics, known as the “Copenhagen interpretation” after the home city of Danish physicist Niels Bohr, one of its architects, holds that particles play out all possible realities simultaneously. Each particle is represented by a “probability wave” weighting these various possibilities, and the wave collapses to a definite state only when the particle is measured. The equations of quantum mechanics do not address how a particle’s properties solidify at the moment of measurement, or how, at such moments, reality picks which form to take. But the calculations work."
(Unfortunately, in trying to search for answers, I'm confronted with claims that "quantum mechanics" has such accurate predictions, that it must be true.  But what does that mean?  Do they mean that the Schroedinger equation has accurate predicitons?  Or something else?  I'll have to dig deeper to see what they are referring to.)
===Distilling these items from these articles into identifiable controversies etc.===
*What, if anything, causes the probabilities?
*What happens when you measure something?  Why does the thing seem to switch from a wave to a particle?  How does this switch happen?
*How does "entanglement" work?
==My interpretations==
The accurately labelled stuff (quantized energy, quantized particles) isn't puzzling enough for me to worry about right now.
The seemingly random stuffthat is innaccurately labelled "quantum physics/mechanics", on the other hand, is much more challenging or puzzling.
I suppose, like all physics, they do seem to be about things interacting, and what happens when they do.
*wave-particle duality (might as well be a duality between being quantized sometimes but not other times. When? Seems to have to do with interactions/"measurements", but why?  How?)
*uncertainty principles (since this has to do with measurement, see the other one about measurement below, maybe related)
*entanglement/coherence (I think this is just the information caused by interaction between things, combined with determinism)
*(supposed) superposition (which is just what is posited to be the state before the probabilistic behavior, before a measurement)
*probabilistic behavior, when a measurement is done, the value measured seems randomized
*"information"? (just another term for the results of interaction?)
*measured values being caused by the method of measurement (I think this is just interaction between things, like measuring the position of a grain of sand by touching it)
And the main controversies:
*What, if anything, causes the probabilities?  (they do seem determined, the "waves of probability" do behave like our familiar, classical, deterministic waves, right?)
*What happens when you measure something?  Why does the thing seem to switch from a wave to a particle?  How does this switch happen?  (maybe there is no switch, but then why does it seem like there is?  This would lead back to figuring out what the cause of the "waves of probability are", which are the only reason the particles "seem to behave like waves"?)
*How does "entanglement" work? (see my comment on entanglement above)
==See also==
*Here's the wikipedia introduction to "quantum mechanics" for laypeople like myself.
*CliffNotes summary of quantum mechanics
*Summary of Important Ideas in Quantum Physics