Why is it we all assume the turbolifts can
only travel vertically or horizontally.
I think mainly because the turboshaft network is portrayed as perfectly rectangular in graphics from ST:TMP on. But no doubt there are exceptions here and there - and the TOS ship certainly is famous for angled features such as the chutes Scotty is always climbing up to access this system or that. And a turboshaft following the contours of the connecting neck would indeed make a lot of sense. Although the rows of windows there place rather strict limitations on that, and would better match the idea of a perfectly vertical shaft just ahead of the vertical stack of windows. Otherwise, there would be very little space between a window and the turboshaft.
That could explain the long turbolift ride in "The Enterprise Incident" when Spock takes the female Romulan commander to ... the cargo hold in the engineering hull?
Whether we see a long turbolift ride there, or merely a long, dialogue-heavy scene that begins with a turbolift ride, is something for the viewer to decide. Certainly the signs of ongoing turbolift travel, such as visibly flashing lights in the background or distinct turbo-travel noises, disappear almost immediately after our protagonist and antagonist board the lift.
It just seems a poorly contrived theory of why the turbo shaft as seen from the outside of the ship sits at the rear of the bridge, while the internal doors are offset from the rear.
We have strong reasons to insist that bridge turbolift station placement in the TMP-refitted ship is completely arbitrary and can be changed by two men with antigrav grapplers in half an hour; any position from "directly aft" to "directly to both sides" is available. It thus doesn't really pay off to insist that the TOS ship bridge turbolift placement would be nailed down by some external feature...
If we interpret that stern-facing bump as a turboshaft, then we could argue it's an extension of the main turboshaft up from the bridge level, intended to enable the lift network to be connected to another, from a fellow starship or a starbase. And wherever the bridge turbolift would be located, it would be
off to the side of this shaft, so as not to block the passage.
...what are the purpose of the handles? Sometimes people seem to grab and twist them, other times they don't. Are they some type of manual control?
Many episodes would allow us to interpret them as "dead man's handles" of some sort: you can't give the lift a voice command unless you simultaneously twist a handle to indicate you
really mean it. That way, you won't be crushed by the doors if you discuss last evening's exciting game of BRIDGE while stepping aboard, or spread the latest rumors about what Ensign Jawline and Yeoman Softfocus were doing at SICKBAY while stepping off.
However, this doesn't cover all the bases, especially the ones where nobody gives a voice command. OTOH, the handle doesn't appear to be a convenient selector for complex orders such as "as close to Cabin 7G221 as possible" or "Deck 16, forward port station". Perhaps the system is smarter than we give it credit for? Perhaps the turbolifts run on regular, predictable routes like a bus,
unless you specify a destination, and the handles are for activating or overriding the bus functionality.
Timo Saloniemi