So, who did fire the weapons? Navigator or Helmsman?
My take: the Captain takes the first step in firing the weapons, by calling "Fire!". The gunners down at Phaser Control and Torpedo Control finish the process, by throwing the appropriate switches. And whatever happens in between is by mutual agreement.
That is, the two guys or gals at the center console decide which of them will send the signal down to the little folks at weapons control when they have the enemy in crosshairs. Or the Captain may specifically ask to be patched directly to weapons control, so that his word is enough to launch the volley. Yet the little folks ultimately decide whether or not to act, as firing an overheated phaser or a half-loaded torpedo might be bad for the ship.
That's much like it worked on those WWII warships that were the model for so many things in Trek. And that sort of man-in-the-loop design makes great practical sense when your weapons are as malfunction-prone as, say, the phasers in "Balance of Terror".
When did we first hear of Photon Torpedoes?
TOS "Arena".
Or, by the internal timeline, ENT "Sleeping Dogs", where it was established that Klingons had the technology first, and invented the name. Indeed, the name may actually be something of a mistranslation from a Klingon term that makes more sense...
United Earth Starfleet put photon torpedoes in use in the mid-2150s already, so we might assume that they were standard gear in early TOS episodes as well, and not some sort of a hasty refit just before "Arena". There simply weren't that many occasions for Kirk to fire such weapons in early TOS - "Arena" was the first actual space combat episode after "Balance of Terror".
Timo Saloniemi