I think it is most important for a teacher to play the pieces and studies that are being played by the student.
It is normal to be nervous.
You can sightread better if you know your scales and arpeggios.
Never just run through a study because you happen to be familiar with it, but use it to see what you can get from it on this new day which has been granted you.
You cannot prepare enough for anything.
The mind of the performer is a very strange thing.