Things I find important in flute playing...
You can never stop listening for pitch. Hear and adjust every note, even when playing alone. When playing with other instruments, take the attitude that adjusting is YOUR job. Pitch on the flute is pretty bendable--be thankful!
A colorful sound projects well, without forcing. When working on tone you should strive for a clear tone, free of air noise, yet one that is rich in overtones. To develop a good tone you first have to have the concept in your mind. It helps to listen to as much good playing as you can when you are learning.
You have to decide where the phrase is going. Where is the peak? Every phrase should have shape, created by dynamic shading, sometimes large, sometimes subtle ("micro-dynamics"). Indeed, almost every note should be either going somewhere or coming from somewhere. Rarely would you want several notes in a row to have equal importance (i.e. the same dynamic.) To make these decisions, you might need to study the score and identify the harmonies. I like the meter of a passage to be very obvious dynamically. A downbeat should sound like a downbeat, a pick-up
like a pick-up, unless there is a reason.
Vibrato: strive to produce a free, loose vibrato, and then learn to use it with control, and sparingly. It's a really good exercise to play a phrase without ANY vibrato, but use the dynamic shaping to make it as musical as possible. Another good exercise is to play the phrase and make sure EVERY NOTE has vibrato, with a smooth legato connection between each note. Careless vibrato can obscure the line, but well-executed vibrato can enhance every aspect of the delivery. It's ironic that making classical music sound spontaneous, original and alive takes careful planning and control of all the small details.
Non-musicians would probably be surprised to know that classical music, played well, has much rhythmic freedom. This rubato, though often subtle, further enhances phrase shape and expressiveness.
To cope with nerves/stage fright it helps me to tap into a feeling of "joy". I've gotten some helpful techniques from a book called "Mental Toughness Training for Athletes" by Loehr. It also helps when I focus on my breathing techniques and stance, and all the physical tricks which make it easier to play.