I realized halfway through answering that the topic is a month old but whatever! not letting it go to waste

1.) Would you rather have a campaign full of new and untested ideas or tried and true ones?
One criticism of Blue Planet Act 3 was that none of the missions were really standard fare and people were pretty divided if this was a good thing or not. Is a mix needed instead, sandwiching more normal missions in between radical ones? Do radical departures of gameplay just hurt a campaign? To have fun, would just simple missions with "attack this" "escort that" "scan over there" be enough?
I'm fairly conservative in this regard and a firm believer that if you are gonna do something "crazy" it should be because your storytelling requires it, not because you simply can therefore you must make a mission to justify your new toy.
Sexps and scripts are tools to bring life into your story not the other way around.
2.) Do you tend to view your interaction with a campaign as a strict "first-person-like" affair (you are the character), or a "third-person-like" affair (you see the story through the character's eyes, like a book). Or do you change your interaction based on how the campaign expresses the intent? (aka the don't care option)
There's the age old debate of silent vs voiced protagonist and FreeSpace has its share of both in its many campaigns. But ones that take a voiced protagonist approach sometimes receive the criticism, "the player character would never say what I would!" or "I didn't really connect with any of the characters" and say it detracts from the experience. Do you think these come from the style used, or just bad writing? (Or would you assume the role of the Player Character, even if they make decisions that you would not.)
I tend to put myself in 3rd person mostly because your decisions hardly ever carry consecuences in freespace campaigns so its hard for me to care about what I'd do instead of just playing along and see where it leads.
Grats on saving 100% of that civilian convoy alpha 1, here have a medal (in the rare ocassion you do get one). Or grats on scanning that cargo container out in the middle of no where instead of shooting stuff which would've made the mission much easier and fun, 2 missions later... there's no new weapon in the loadout screen, no extra wingmen, no extra reinforcements or that extra aeolus to guard the flank of your *next* escort mission, even if you have to spawn an SSM strike to kill it for balance reasons at least the player feels like his actions had meaning.
As for characters specifically I don't think many campaigns have taken the time to develop a characters deep enough to really care for, Blue planet being the exception at least for me, sorry if this offends anyone I have not every campaign ever made so...
3.) How important is a story? Are you just happy with a flimsy pretense to shoot up rebels and kill Shivans? Or do you need an elaborate political crisis and motivation to go to war?
Does it need to culminate in a galaxy-spanning event, saving all of humanity? Does a story need to make concrete amounts of sense or can you still enjoy a light story by just rolling with everything?
I'm a sucker for galaxy spanning event campaigns so I'm pretty biased here. But lets say that your campaign isn't.. at least for me it would have to make up in other areas such as gameplay, story, characters or motivations.
Say for example... your campaign happens in some remote sector with little to no contact with some kind of military / goverment / corporation then you probably can't pull some major capital ship battles, in this case each ship should be important, the player should consistantly fly with the same cruiser, talk to the same captain, hear the same awacs officer to maximize the assets you do have available and make it all that much bitter when you lose them.
The story should be very character driven, lots of conversation with your wingmen etc.
4.) How much effort should be used to create a setting?
A campaign author may spend hours writing on how and why this planet has a problem with syndicate crime, detailed dossiers on important characters, or timelines that explain the human race from World War 2 to the Neo-Terran Conflict. Is a background necessary to enjoy, is it a bonus, or just words that you'd rather not read unless absolutely required? (Or would you like to read things, but FreeSpace's awful interface font prevents you from doing so?) Is putting any of the setting establishment into the campaign a good thing, or should it all be regulated to optional reading?
Background information is always good, the player can always skip it. Its how you present it to the player that matters most with freespace and the interface is a huge problem but there are ways to minimze the problem.
What I hate the most is getting thrown into a campaign with someone expecting me to read 10 tech room articles just to understand whats going on, stuff needs to be sumarized to the player in the fiction viewer or briefing and depth added to it in the tech room, not everything in one place or the other.
If your campaign is not set in the canon freespace universe just do a small cutscene (just text will work fine) explaining to the player quickly what your universe is about, if he truly cares he'll go to the tech room and read more about it.
In your particular example crime is the same everywhere, there's no need to explain it too much, money, power, ideology etc... what should be important is explaining how the head of the syndicate thinks, what are their resources and how they are affecting the player character and those he cares about.
Depending on the type of story you are trying to tell the background will be meaningless or everything so I think this is up to the designer to gouge and see if his time is better spent on other aspects of the campaign.
5.) How important are the structures/orders of battle?
By this I mean, should the campaign authors have a definitive list of active assets in a theater and only use them, or just smack down any number of corvettes as the mission needs corvettes to attack. Should we ever find a destroyer with no capital ship escort or a cruiser in the middle of nowhere just being there to be attacked by someone. Should each battle mean something to the story, or can some be there for some pleasurable blowing up time that doesn't change the story or tide of battle.
I think its awesome to take the time and figure out the resources available to the player's faction/allied factions. Losing a destroyer should be important, not just... oh there goes another 10k people, bring the new player base of operations and change his squadron!
As far as ship operating as individuals or battle groups that depends a lot on the campaign. But in general no destroyer should ever be by itself, these things are supposed to be the equivalent of an aircraft carrier, its not something you can just throw around and hope for the best (Except in super dire situations).
Everything else is fair for me, but I do prefer for ships to work as a group, more realistic that way, with that said when **** hits the fan some amazing things can be done with a random leviathan jumping in to save the day.
6.) Should a campaign be about something (a theme, a question) or do those literary devices just belong in other media and not games? Does any attempt at symbolism or dramatic devices just take away from the enjoyment of a campaign?
They can be added and add enormous amounts of quality if done right but you shouldn't try to make the player feel like he has to change his life because he played your campaign imho.
7.) Does the use of generally known music hurt the enjoyment of a campaign? Do you just think of the original source instead of the campaign?
I don't think so, music is basically emotions translated into sound waves so as long as they are used at the right time it won't matter if you've heard it before or not.