1) See answer for #2
2) If all the rules and laws of the universe work the same, I would guess constants stay the way they are due to inertia. Just as an object will continue moving in one direction until acted upon by an outside force, as far as we know a constant does not change until acted upon.
3) Having only one data point for each category to study wouldn't yield much information. We would need access to many, many universes to even begin to determine even the most basic guesses about constants.
If one of the universal constants could be changed... would we even want to? Changing something could be disastrous. Think about the gravitational constant. An increase to the force of gravity would cause poorly made structures to collapse. It might kill plants and possibly some animals, and would require most of structural engineering to be relearned to deal with more downward pull. A reduction in gravity could have devastating effects on our atmosphere. If we could change a constant... should we?




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