This is true only at a very zoomed out scale that misses some key issues, as I will try to explain:
What are the limits on what they can ask to do? What narrative authority do they have? Can they declare actions, or goals, or acceptable outcomes? Who frames 'the current state of fiction' in the first place?
With one exception, the current state of the fiction follows on from whatever it was before. That one exception is the very start of the campaign, at which point someone kinda has to set a genre-appropriate scene as a backdrop.
Your other questions there are the sort of detail I'm trying to strip away in order to define the fundamental play loop that underpins it all. Once that's defined, then we can argue about what types and degrees of details to overlay upon it.
Who decides whether or not to consult the resolution engine? What conflicts can it resolve? What kind of result can it generate? What influence if any does each participant have on the outcome? Can any participants override it altogether?
In sequence:
There's no decision. Every action no matter how trivial has to go through the game's resolution engine, even though in many cases it might not be obvious that it does so. Silly example: player declares that his character will put on her boots. GM says "fine, your boots are on." In between those was a tiny but not-zero reference to the resolution engine, in this case the GM deciding the action is an auto-success and jumping straight to narrating the result.
The next two questions again speak to extraneous details overlying the root play loop.
The last two questions are fine-tunings of who or what might (partially or fully) comprise the resolution engine.
Who is that 'someone'? Is it always the same someone? What factors do they have to take into account in their narration? Can they just describe, or can they interpret? What can they ignore or double down on? Can anyone else veto their efforts?
Again, more fine-tuned details that overlay the root play loop. Description often cannot be done without interpretation so there's no either-or there. Vetoing narration sounds more like a part of the resolution engine, as actual (as in, binding on the fiction) narration can't occur until the resolution engine has finished its work.
Who gets to frame the transition back to 1? Who gets to decide what 1 is?
Without a transition back to 1 (player(s) declare action(s)) the game probably ends.
As for who gets to decide, I think that's covered by the very essence of what an RPG is: players roleplaying characters. A non-avoidable part of roleplaying a character is deciding (and then declaring) what it does in the fiction; and even if the character does nothing at all that's still an action declaration even if maybe unspoken.
This really feels like saying all movies are the same, just some noises and movements of images that in the end come to a stop. I mean, yeah, kinda, but a whole lot of relevant factors are being overlooked.
Perhaps. What I'm after is to strip it down to the studs: what makes an RPG tick. Someone (was is Manbearcat? I forget now) said upthread that different games have greatly different play loops; I'm trying to say no, this is not the case; all they have are different details overlying the same fundamental play loop that every TTRPG has. In order to say this, it's only fair that I try to define and delineate what that underlying basic play loop looks like.