RA-
1. Yes, but lots of other things as well in natural waters, even more in our tanks which are also relatively high in organics.
2. Yes, Ca++ and MG++ have nothing to do with pH.
3. Yes, and severely misunderstood in the hobby. Fish are sensitive to osmolarity.
4. Same as above. You can change the pH without significantly/detectably affecting the TDS - think about CO2 supplement.
5. Yes, also BW and estuarine fish.
6. Yes, but incomplete. We have processes going on in our tanks which do occur as such in the wild - the build-up of nitrogenous waste products and of organics is many-fold greater in captivity, and the biological processing of those and/or the chemical results of those are many-fold magnified in capitivity due to bioload issues (we have many-fold the biomass in out tanks as in natural waters). Don't expect straight high-quality (low TDS/high-resistance) RO water to support a tank. Supplements are needed. BTW, most but not all blackwater fish do fine in higher-TDS waters, but may not breed. Their egg membranes are harmed by Ca++ & Mg++.
7. Yes, but commonly suggested tank conditions may or may nor be the best for particular fish. Mollies for example are commonly suggested for NaCl-added tanks, but salt does not buffer the water upward, only adds TDS. Not all TDS is equal.
8. Yes.
9. Maybe. "Alkalinity" or buffering is better. The titration does not read just HCO3/CO3, but others as well. In the wild, it is primarily bicarbonate/carbonate. In tanks it can be a lot of other things as well, and can be affected by organic and inorganic acids present.
Not really, they are measures of only part of TDS. Sulfates, chlorides, sodium, potassium, etc. are common and do not read on GH or KH. GH/KH may provide hints that water is relatively hard or relatively soft, but concluding that to be the actual case is unjustified.
If you bring the tank water up with coral/aragonite/bicarb, and you replace it with large % volume partials with low TDS water (tap or RO), you most definitely do risk osmotic stress to the fish - a specialized case resembling OTS. Options include more frequent smaller percentage changes or pre-treating the replacement water. Water mods are rarely a fast, simple, or cheap process.