Partial Answer (mostly complete except for the subtle&moderate hints): following the hints by Jens and Stiv, the three are (it also explains Decisive Hint 4):
The United States, Liberia, and Myanmar, the only ones that do not use the metric system/SI units.
Critical Hint:
It refers to the famous Mars Climate Orbiter. "An investigation attributed the failure to a measurement mismatch between two software systems: metric units by NASA and non-metric (imperial or 'English') units by spacecraft builder Lockheed Martin."
To be a little blatant, I actually figured out the connection to SI units and chemical elements (to come later) before I read the hints :) But thanks for the hints still.
I will explain the 7 things in order, and talk about the hints when they become relevant in the discussion.
The seven things referred to in the text are
SI constants. Figuring out the SI system was such a red herring, since SI has exactly 7 base units. I spent a lot of time trying those, until I realized that there was 7 constants involved in the redefinition of SI base units in 2019.
and their symbols are simultaneously (or partially related to)
Symbols of chemical elements in the periodic table, with one "exception" for the fifth which represents an electron.
The first one is
Chemical Element: Cs or caesium, the single stable (i.e. no stable isotopes/"not radioactive") element with the least electronegativity, hence the most positive.
SI constant: $\Delta\nu_{Cs}=9192631770\ \text{Hz}$, the ground-state hyperfine structure transition frequency of the caesium-133 atom, used to define second. I included the number so that people might work on the subtle&moderate hints.
Regarding Decisive Hint 2:
I believe it refers to Po/Polonium, discovered by Polish scientists Marie&Pierre Curie. However, why is it the first? in terms of atomic number, Technetium/Tc is also unstable and precedes it; even if we disregard this artificial element and only consider the natural ones, Bismuth/Bi (the one before Po) "was discovered to be extremely weakly radioactive" in 2003. I have seen older textbooks that still use Po as the first one, though I personally think they should have been updated.
The second is
SI constant: $c=3\cdot 10^8\text{ m/s}$, the speed of light. In special relativity, it is independent of the chosen (inertial) reference frame.
Chemical Element: C/Carbon, a well-known non-metal element.
Decisive Hint:
The speed of light is currently known as the fastest physically possible speed.
The third:
Chemical Element: H/Hydrogen, a non-metal element. Non-metal elements can form covalent bonds, which requires orbital overlapping. (not 100% sure)
SI constant: $h=6.63\cdot10^{-34}\text{ J}\cdot\text{s}$, the Planck constant.
The Fourth:
SI Constant: $k=1.38\cdot10^{-23}\text{ J}/\text{K}$, the Boltzmann constant. It relates to entropy, and a kind of entropy is called information entropy in information theory. (not 100% sure)
Chemical element: K/Potassium.
The fifth:
SI constant: $e=1.6\cdot10^{-19}\text{ C}$, the elementary charge.
Chemical element: Electron/e/$e^-$.
"The first made you do the fifth" potentially refers to the fact that Cs is the element with the least electronegativity, so it is very easy to lose an electron. (not 100% sure)
Decisive Hint 3:
As explained above, hydrogen and carbon are nonmetals, while the electron is not even an element.
The sixth:
SI constant: $K_{cd}=683\text{ lm}/\text{W}$, the luminous efficacy of monochromatic radiation of the green light, used to define the unit cd (candela).
Chemical element: Cd/Cadmium.
"The first, second, and third made you do the sixth": this is the only part where I am unable to figure out what's going on.
The seventh:
SI constant: $N_A=6.02\cdot10^{23}\text{ mol}^{-1}$, the Avogadro constant. The numerical value is indicated directly in the text.
Chemical Element: Na/Sodium.
EDIT: in response to the hint that
chemical elements
are mostly irrelevant, I'll add few preliminary thoughts (before I work on it more seriously).
Overlappable may refer to bosons, as multiple particles can be in the same quantum state (roughly speaking), in contrast to fermions. Photons are bosons, and their energy is given by $E=h\nu$ where $h$ is the Planck constant, explaining the third. Presumably this also explains why the independent is overlappable since it also refers to photons. Electrons are fermions and more than one of them cannot be in the same quantum state (Pauli exclusion principle), which explains why the individual electrons mentioned in the fifth are not overlappable.