Its sounds like an enhnaced version of Fate/Hero/Courage/Willpower points that characters can 'spend' to gain automatic successes in their actions, or to ignore a detriment for a specific time, except on a grander scale.
That's pretty much it, yeah. In addition, you can use APs to buy special abilities for your character during a campaign, if you have a narrative explanation for it. In general, APs are a rare reward for something exceptional. Players get ordinary experience points all the time, which they save to buy APs or use for normal development. Extraordinary things - like reaching a major personal goal - can get you an Advantage Point directly.
Your rules for the ships, for example: how are you planning that? Like a detailed wargame (like Warhammer), or a stylized higher-level wargame (like War Machine), or an adaptation of the face-to-face combat or some other set of rules, or an abstract "ship events matter if they impact the players walking down the corridors" kinda thing, or something else?
Basically, Gloomships use the same rules as characters. They have abilities like characters, take damage like characters and so forth. There's a different fluff for them - instead of Perception you have Sensors, instead of Agility you have Maneuver - but the logic is the same. Basic mechanics are very similar, just on a different scale. Player characters are part of the ship (presumably officers/specialists) and their personal abilities matter in what happens. The ship rules are meant to be used in situations where you want detail at that level. You don't need them for abstract ship events that happen to singular characters inside the ship. You have the basic rules covering that already. Though even if you run a very narrative campaign, you can benefit from the extra depth and content something dedicated to Gloomships would bring to the matter.
All this being said, like I said, strategic and ship rules are just drafts waiting for the future. They haven't even been playtested yet for that reason. I'm concentrating on getting the basic package done and out first.
Also, when you talk about player control over their character's narrative, what do you mean (I mean for your ideal)? For example, if the referee rolls up a thing that says my character gets dysentery, can I as the player just say it cures itself? I don't mean the AP thing, of course if a player can create a secret escape passage using AP then he could cure a disease with AP. I meant how much authority does a player have over things that happen to his character? How much authority does a player have over things that his character tries to do?
My personal ideal would depend on the genre and style of the game I'm running. However, if you are asking what is possible in this game... It depends on how you want to play it.
The basic assumption is the traditional sharing of power between players and the GM. This means that the players play their characters. Meanwhile the Game Master, referee, storyteller - whatever you want to call him - plays the rest of the universe. Players have power over their characters, their actions and deeds as defined by the mechanics of the game. They can
try anything, but the
system decides whether they succeed, as refereed by the
GM. This goes another way too. The system exists as a buffer for arbitrary decisions by GM. (Of course, a GM can cheat etc, it all falls down to the style of play. For example, I like to GM sandbox campaigns where I'm the neutral arbitrator, but sometimes I lead very story driven games. In the latter I might fudge the dice to keep the player character alive and so forth.)
In this instance, a dysentry would get some sort of resistance check to see if it sets in. After that it would start inflicting negative effects. The player would need to work according to the rules to get rid of it. This would require treatment with the included treatment checks. Treatment availability would be set by the GM. The characters would have narrative power over dysentry in telling how his character reacts to the situation and possibly in how exactly the damage of the disease takes place. He couldn't magically just declare the disease cured. That would step on GM's toes as the person playing the universe.
Stuff you can buy with APs, in this basic level, grant you special privileges to foray into GM realm. Like curing dysentry - with a sufficient explanation - by spending an Advantage Point. Likewise, you can buy allies. They are NPCs you share with the GM - you can play them yourself on the side or the GM plays them according to guidelines you've put forth. You've paid the APs for their trustworthiness, so GM won't backstab you with them. A character could have a plenty of helpful friends ingame, but the Ally is someone you know the GM won't use to fuck you with.
Now, this is how this dysentry thing would be played with the basic rules. You could play it differently if your define the narrative powers differently. It just isn't the basic assumption.
Regarding authority on what player wants his character do, you tell what you want do and how you do it. The GM sets the difficulty level, the system tells if you succeed or fail and to which degree, GM or player and GM together weave a story on what happened. Pretty standard, I think. So the player has 100% authority on what he wants to do, but no guarantees that what he wants to do succeeds. The game system exists to define what players can do to each other. GM (which I consider the player of the universe) can't affect the player characters (or their Allies) without using the rules, the players can't affect the universe or each other without using the rules. This is of course a simplified example. I really doubt anyone requires a skill check from a player to eat a burrito, even though it is technically a character affecting the universe.
If you use some parts of the rules, there are things which may drive characters act in a way the player might not necessarily want. Basically, there are rules for vices and virtues, passions and addictions, mental instabilities. This means that, for example, a merciful character might not be able to kill someone, even if the player wants to. This is usually resolved with a dice roll to see if the character can act against his emotions. If the player chooses to act according to such drive in a dramatic situation without a roll to resist, he gets a little bonus. This is all optional rules though, for people who want to try such mechanics.