The Pokemon move/attack that always leaves opponents with at least 1 hit point

The Power of an attack directly correlates to how much damage you deal, because its presence in the damage formula is entirely multiplicative. So, an attack with 120 power will do twice as much damage as one that has 60 power. The same goes with your corresponding attack stat: a Pokemon with 100 Attack will do twice as much damage as one with 50 Attack when using the same attack on the same target.

STAB has operated consistently since Gen 1 so this applies to all of the games. It increases the Power of an attack by 50% if it matches one of your types. 60 becomes 90, for instance.

Technician increases the Base Power of an attack by 50% if its Power is 60 or less. So the most you get is boosting an attack at 60 power to 90. This occurs before STAB is calculated, so your Power would be 90 for STAB, boosting it to 135.

Splash will never do anything.

You may either be misremembering your Magikarp using Tackle or Flail, both of which are moves that Magikarp can learn that do damage.

You may have also run out of PP for splash (unlikely I know, who's going to spend 40 moves splashing around to no effect?) then your Magikarp will "Struggle" which will cause damage to both your enemy and yourself.