Finally someone who asks for help on a plot and campaign that actually gives enough information in their first post!
Most of your "issues" can be resolved by some preparation before the campaign starts. The two elements you need to work on with your crew is character weaving (troupe and world) and character motivations.
When you read a story or see a movie, how often are the characters just there, with no attachment or place in the world or the other characters in the setting?
The answer you are looking for is basically "NEVER". (Okay, okay, The man with no name who is not really a character in the movies, but just a force of nature. If you count him as a character, he is the exception.)
Writers know that audiences won't believe characters that are just "plopped" into the world. Things and people need to come from some where and have a reason to do the things they do. (Even amnesiacs soon find a place in the world, being the exceptions to the general rule).
Most players are reasonably good about creating a character conception and history, no matter how lame. It is easier to play a character when you have a strong background behind it and most players like making play and roleplay easier, so they make characters with a strong conception and history. Yet often these stories do not have any attachment to the world around them.
This is solved by character weaving to the world. It is always best to make a character part of the game world, weaving them into the tapestry of the background story. Players should check out the world pack the GM provides ( http://www.rpgcitadel.com/guild/index.php?topic=378.0
). If the packet is not available or the players are not the reading type, the GM should have an "elevator speach", a five minute synopsis of the setting for the game, hitting the high points that are important.
Players should talk with the GM about elements in the game world that the character could have a connection to: recent history (You were at the battle of Kingam Falls!?), NPCs, organizations, other characters, or even just random things. Form a connection to these things and the character is connected to the world. This helps better define the character and gives the player/ character more options in play. As the GM, innocently steer them towards world elements that will be important down the line in the campaign. So the Order of the Oak member finally gets his chance to shine as the Dark Druids attack his order house and he gets to lead them stopping it)
In this case, you would make sure that there were people who in the noble circle, associated with the various circles that are important. Or they could all be part of an group or organization that are assigned to such tasks.
By being part of the world, characters are motivated by their connections and positions in the world. They are no longer doing this "because it is the adventure", they are doing this because it is their job, their obligation, a favor to a friend, their chance at promotion. If you spend a few sessions before such the action really starts just having players work their connection and place in the world, they will have a feel for the "way things are". That way when things change, they will be in a position to notice it and change.
Note: Characters should be important to the world. You can be somewhat important and still first level. The prince can be first level, the ambassador (princess of Alderon) is first level, the smuggler with a history and background (and his fuzzy sidekick) could be first level... they just sound like they are a higher level, and you get the idea.
Back to the movie analogy. So, when you read a story or see a movie (a good one anyways), how often do a group of four to six total strangers, with little to no knowledge of each other, get thrusted together to do something and work together well if they had all been part of a well oiled machine?
The answer you are looking for is basically "NEVER". (Okay they might eventually pull their act together later in the film after some time together)
So why do we accept this in games? They are supposed to be inspired by literature and action/adventure movies. Even video games have a back story explaining why the various characters are working together. No matter how flimsy, there is always a back story to make sense of things.
Not so with game characters. In most cases, they are thrusted by fates into a group of complete strangers to face life and death risks. You would hate this in a movie, why accept it in a game?
So where is your group's backstory?
Some players will say, "Well, they are PCs", so they will interact with characters that normally they would of ignored or run away from. The PC halo is a hackneyed game concept that says, if it is PC you are supposed to embrace other PCs, no matter how weird, lame, or dangerous, the character is. (The concept of halo came from the little bright ring that surrounded characters you were specifically using in early computer RPGs, much like the green polyhedron in a sims game or the gold circle at the feet of a character in most modern games).
Players really want stories, though they will often settle for less. However, if they want a story that includes their characters, they should work with the GM to make it happen.
First and foremost, they need to have a "Group". To make a group, there needs to be some kind of relationship between the members. The Character must be weaved together, not only weaved into the tapestry of the world, but into the tapestry of the group.
The weave for the troupe has two parts: metagroup and group. In terms of the metagroup, this is the group of players getting together and doling out campaign roles (Who fights, who sneaks, who thinks, who smooth talks, who leads, who is the back up should someone else be "indisposed". The group weave is a bit more complex.
To help the campaign story along, work with the other players when you create your characters. Find a connection, something in the characters' mutual past that links the characters together. When did they first meet? Did they work together? Did they grow or attend school/ training academy together? Do they have a mutual friend? Was one character the best friend of another's older sibling? Did they meet once at a party? The more connections and history a character has with the other characters, the easier it will be to play with those characters. Your character will have a reason to work with the other character, rather than the lame.. "well he is a PC".
Now even if the troop is meeting each other for the first time as the adventure starts, lets say the smuggler (and his furry sidekick) and Paladin (and the Last Hope-Paladin in training, these characters should be (approximately) balanced as a group because of the metagroup, but the players should also plan on the characters being able to interact with each other on a personal level. Even if the reaction is a "Friend-Foe" one (like Spock and McCoy in STOS or Dr.Who and Tristan (early on), the players will be able to interact and function together.
Excuse the explanatory excursion here: The GM should always be involved in character creation. Not only will they supply information about the world, but they are a source of ideas about characters as well. They can make sure each character has a protected nitch and that ever character will have something to do in the campaign.
One other thing they can do is run mini-weaving scenes: Players play out or narrate scenes between their characters at sometimes in their histories. This gives them a chance to practice their characters and develop a mutual history.
The various weaving process gives the troupe reasons to be together, some depth to their relationships, and the chance for the group to work out who does what, in addition to adding depth to the character's history and the GM's world. The GM should work with the players to see how the characters are woven together.
I always recommend a cast party, where players make their characters (or finish their characters) together. This of course goes beyond mechanics, but into conception and meta-troupe options.
Character motivations, we finally focus on those. People do things for a reason, usually a good one (in their mind). You need to give characters one to three strong reasons for doing what they are doing (getting involved in the current or future story arc), otherwise they will get bored during a slow part of a campaign and either leave or just express "a lack of enthusiasm"... killing or stalling the campaign
Goals are based on your place in the world (see character weave to world), relationships (history or troupe character weave) or personal need (see character's personal conception). . These motivations are goals, many of them concrete and taking several steps, that the character is striving for. These should stem from the character's conception, but they can be picked up in play.