It's a bit dubious whether the standard mode of TOS shuttle sublight propulsion would involve rockets at all. Chiefly, if the standard rocket flame is invisible, it would be quite difficult for Spock to make it visible without special preparations. "Dumping fuel into the flame" is fine and well as such, but as said, there is basically no fuel left for the trick... Will the tiny amount really make a difference?
Again, I think we are looking at a colloquialism that refers to a nuclear fusion reactor that foremost produces energy
TOS has a great illustration of that dilemma in "Balance of Terror". The Romulan commander always has to decide whether to use his "fuel" to produce energy for the cloaking device or to use it for propulsion thrust.
Not quite so strongly agreed. The Commander doesn't really have a choice: the ship grows visible against his will as power wanes. But the two systems competing for the power are not specified to be drive and cloak. Rather, it seems that it's the weapon
that eats power and consumes fuel so that any other systems are compromised, both temporarily and in the long term... Use of weapon results in dropping of cloak and cessation of movement, actions that the Commander would not willingly take unless the shortcomings of the technology thus dictated. But combined invisibility and movement are possible throughout the episode.
Agreed on the general sentiment that technology shortcomings that force the heroes or villains to choose are excellent for drama.