The short answer to your question is "no". There aren't any missions. FS 2004 is a simulator not a game so there aren't any prepackaged missions except for a few "Flight Adventures" like the ones mentioned above.
That's the bad news. The good news is that being a simulator FS 2004 is far more open ended than a game with prepackaged missions. You fly where, when and in whatever aircraft you want. No limits (OK very few, you can't fly to the North and South Poles but everything else is fair game).
You can however pick up flight adventures online either here at SimV or other places like AVSIM if that's what you like. Not sure how many there are but I've seen them. Don't usually like that sort of thing myself.
Something you can do alternatively is earn ratings just like in real life. You start as student pilot and train for your PPL (Private Pilot License). FS 2004 has lessons where you fly with an instructor and practice the skills and later fly with an examiner to earn your license. The lessons go from PPL in the small planes like the Cessna to ATP (Airline Transport Pilot) in the heavies and the check rides are very difficult to pass.
Back to your original question. If you want to fly passengers the best option is to join a virtual airline. There are all types from flying heavies with hundreds of passengers to ferrying tour groups in helos. Different airlines have different requirements to fly with. Some require you to earn all your ratings before joining and others are open to anyone who has the sim.
For myself I happen to be the backwoods outdoorsy type so I've hooked up with an outfit called BFU (Bush Flying Unlimited)
http://bfu.avsim.net/we operate in the remote regions of the world flying old beat up vintage airplanes as well as modern short field capable craft in some of the damndest weather conditions you can find, hauling everything from passengers to dog food. It isn't anything packaged with the sim but it provides something to do with it and I think it's much better this way since the virtual airline is whatever you make of it which is something that Microsoft could never do.
