Hitler was not good, much less great, for technology. Germany was the scientific center of the world before the Nazis took power, so their successes are mostly attributable to inertia. The Nazis destroyed this on their own with the 1933 Nuremberg laws.
Yeah, it is different, but once you know what you're after you can measure. It's a "type error" to ask for the number of bits of entropy in a baseball, but if you ask for the bits of entropy of a baseball given everything you know about the baseball (i.e. mass, composition, temperature), then you can measure it. You could even design a special instrument which makes relevant measurements of observable quantities and then calculates the entropy of a given object from those.
Temperature is actually defined from entropy, it's the change in energy per change in entropy. So it too is inherently subjective. One way to think about this is that to a simulator or god outside of our universe, who can precisely see everything happening in the universe, the temperature and entropy of everything is exactly zero (of course, they would be able to predict what we would measure it as). To them, they would see the level of a thermometer as simply a mechanical consequence of all the particles nudging it to that exact place (like you would if you saw someone pump the mercury up the tube -- you wouldn't conclude it must have gotten much hotter suddenly).
Entropy is a measure of the uncertainty that an observer has over the microstates (i.e. the exact state of every atom) given their knowledge of the macrostate (i.e. what they are capable of describing: like "the water is just above freezing"). So it's inherently a subjective concept. The most common unit for entropy is the bit, same unit as information.
Anyway, entropy is measurable just like any other physical quantity. You need to determine what your model of the microstates is (often an "ideal gas", with independent molecular point particles with their own positions and velocities, and all interactions are perfectly elastic collisions), what you currently know (stuff like type of gas, pressure/volume/temperature), and then there is a clear answer to what the entropy is.
The true law underlying the second law of thermodynamics is conservation of information. In (classical) physics, this is typically cast as Liouville's theorem, which shows that the area of the phase space of a system must remain constant. (In quantum, it's only true for unitary transformations, which may or may not be everything depending on your interpretation of QM).
Anyway, if you're curious about learning more, I highly recommend http://www.av8n.com/physics/thermo which is an amazing online (and free) book that clarifies the concepts of thermodynamics brilliantly.
One of the major aims of physics is to try to describe reality with mathematical constructs.
If you start with what can be directly observed or experienced, then that's phenomenology.
Those are both valid and interesting ways of trying to understand reality, and I believe they are ultimately fully compatible with each other. But I think you are trying to hold physics to phenomenology standards in a way that doesn't make sense. No one thinks that Newton's theory of gravity "lost contact with empirical reality" because it doesn't have measurements or people as ontological components.
Anyway, that's all beside the point I was trying to make, which was just that the description of the MWI in the article was plain wrong.
"The Many-Worlds Interpretation has it that each time we make a measurement, reality splits into several alternative versions, identical except for the measurement outcome."
That's not right, the Many-Worlds Interpretation is just that the wavefunction in the Schrödinger equation (or its generalizations) is real, and it rejects that there's a separate process that somehow collapses the wavefunction to the single "branch" we perceive ourselves to be in. At the metaphysical level, there's no splitting involved, and no ontological measurements either (much less a "we" to do the measuring).
Nope, black holes have entropy proportional to the surface area of their event horizon. So the more stuff they engulf, the more their entropy increases, and thus they satisfy the 2nd law of thermodynamics just like everything else.
The Bullet Cluster (https://en.wikipedia.org/wiki/Bullet_Cluster) is a big reason why: it's a collision of two clusters of galaxies. We can see where the gas and stars are, but gravitational lensing indicates the bulk of the mass is elsewhere.