I'm assuming a few things when I write this, so please forgive me if these ideas aren't applicable to your topic.
One of the biggest questions I have is what is the say...metagame, of your game? Perhaps that's not the right word. You have a predefined 'strategy' where AI Admirals lead fleets of ships to accomplish tasks in a number of ways. However, what are some of the long term means of accomplishing your task of conquering the galaxy?
Are the turns slow and meticulous, meaning that not a lot happens during each turn, IE, your scouts get spotted and a battle begins, but you have plenty of time to route them away from their massive fleet that's bumbling about, or do you just get a message telling you that they've been spotted and promptly stomped in to dust? Is the game going to take long enough to where research is something real that you care about, or is it just about using the ships you have / persuade to be on your side to duke it out and hope you manage them well enough to win in the end?
How much in detail do you want the battles to be? Personally I think having turns be small periods of time would be a better thing seeing as it allows for more 'tactics' in traditional combat. Though, this kind of depends on what the typical ship is like and whether it would make sense in the realm of turns for the rest of the world. To explain better, combat between a squad of space fighter jets would probably not last as long as combat between space battleships, so to speak. It kind of depends on the world that you want to build and the feel for the game. Having battleships slug it out for multiple turns is feasible if a turn is a couple of hours, but doing the minute per minute turn that dog fighting would likely be manageable with seems really tedious, and would probably be suited better to a more tactics style game (Final Fantasy Tactics, those kinds of games).
I'm just trying to imagine what combat would be like when two similar sized fleets collide with the intent of killing one another. Sure, there are pros and cons to the admiral leading the fleet, and fleet composition, (Which I think you should rethink a bit, but I'll get to that.), but what is there to do other than to watch them duke it out? Would the battle be a single turn, or would it be Mount and Blade style (I'm sure there are other games that do this)? In M&B, when an NPC battle begins, every 'tick' of time that passes the armies would lose an appropriate number of troops depending on their relative strengths, and the weaker / stronger army might retreat and pull back based on any number of things (Horse riders can flee foot soldiers, but the opposite is not so true. A larger army can almost always pull back from a weaker force even if slower, mainly because engaging is pretty much suicide for the smaller team.) Would the player have time to react with another admiral / fleet that was close by, or would there possibly be actions that could be performed on a more micro level to help out the combat. You made mention of having different squadrons and such of unit types...
That brings me to your fleet composition. I'm not designing your game, so perhaps I don't know how simple you want it to play. (Maybe this is for mobile, so having tons of stuff rather than a little slider that decides their 'budget' isn't really an option.) If I were doing this myself, and possibly to give you some ideas, here's what I might implement.
Ship Types - There are perhaps 4-5 different classes of ships, each with their own unit of 'size', a concept I'll get to in a moment. Things like Battleship, Cruiser, Destroyer, Space-Artillery, Frigate (Basically Scouts) might be appropriate.
Ship Size - Each of those types has their own size. Battleships and Space-Artillery would probably be the biggest of the group, followed by Cruisers, Destroyers, then finally Frigates. This is what determines how big the fleet is when they're combined (10 Frigates = 2 Battleships in relative size, something akin to that. )
Fleet Size - The total size of the fleet. Split in to 4-5 groupings. (Tiny, Small, Medium, Large, Grand/Huge/Whatever) Maybe if you don't have perfect intelligent you'd get this, or a range? (Smallish Fleet, which could be Tiny or Small, that kind of thing) I don't know if this would be relevant, and so it might not be applicable to your vision. Though, this could come in play with your admirals. I don't know how important they are to your game, but I've become very attached to the idea of having 'people' that matter leading armies that don't. Maybe some admirals are better at leading tiny and small fleets, and get bonuses / special tactics that they can use while in such a thing. Perhaps the fleet size restricts actions they can take? Huge fleets can do sweeps of an entire area with great success, while tiny ones could perform reconnaissance missions and things of that nature?
This brings me back to the combat. Perhaps it would be neat to be able to split a fleet at any time, but ships that are moved to a new one suffer a penalty for not having a proper admiral? Or maybe you can just do this whenever. Say this particular combat will take six turns to finish, and neither side can flee effectively, so they're going to duke it out to the death. Could you split a fleet and tell a few ships (Think two Huge fleet groups initially, then one side becoming a Tiny and a Large respectively) go elsewhere, only to round about on the next turn and flank them? Maybe that could just be a special action the admiral could automatically perform, but that doesn't sound very 'fun' so to speak. Maybe that's just me, and perhaps I'm going to much in to the micro, which might not be what you want for the game. Maybe they should do that automatically, or perhaps if you didn't have another group nearby you were hosed and shame on you for putting all your eggs in one basket.
This whole idea kind of ties in with your 'fleets being made up of squadrons' that you mentioned above mind you, so if you don't think that's a good idea, I'm not sure how applicable this all is. An iPhone/Android game? Yeah, probably should keep it simple and determine fleet composition some other way than micro-ing ships to a fleet (Unless that's what you really want of course! Not saying it can't be done, but it would be a very 'rich' phone game in comparison to others). Dekstop? I'm sure there's a game someone made where you manage 1000 ships down to the individual crew member, so doing small groups of Cruisers and Destroyers to more than manageable.
