Let me just give some input to #3
I shot these images using a Canon 7D with 70-200mm f/4L IS lens...
a. Stage lights should give you the most dramatic impact. However the colored stage lights sometimes don't work well for dancer's portraits. As in this image:
When I shot this dance performance in Xi'an China, I was shooting with a Canon 40D and using ISO 800 which allowed me to get this image at 1/250 second # f/5.6. ISO 800 is about as high as I would normally go shooting with the old 40D. I was still able to get some decent shots...
1/250 us the slowest I would go for a fast moving dancer. In the above shot while she is pretty well stopped by the shutter speed, her arms are a tiny bit blurred. I like that combination because if conveys action...
With a newer model camera, I would have no problems shooting at a higher ISO. I would rather experience a bit of noise than a blurry image. EXCEPT: if I wanted to achieve a really blurred image to give the illusion of motion by shooting with an unusually slow shutter speed. Noise can be somewhat controlled with PP...
b. Another trick is to shoot the dancers when they pause or at the peak of action. Peak of action is when the subject is, say, leaping; to catch that subject at the height of the jump a the split second when he or she has reached the zenith of the jump and before the dancer begins to come down. In that split second (often difficult to catch) the dancer is still and can be captured at a slower shutter speed. This can also work in sports photography like indoor basketball. Here is a shot when the dancer paused...
c. If you have rapport with the company, talking with the lighting person might result in the lights a bit brighter than what they would be for a normal performance.
d. If you an get the dance company to pose for a portrait mimicking the dance that might be the absolute best way to get the images. You might even be able to go up on the stage for some shots. Shooting in Programmed or shutter speed priority with flash (possibly at -1 or -2 stop FEC) would give you a relatively good balance between flash and stage lighting. However, I would not use straight-on flash. I would choose a Joe Demb Flash Diffuser Professional with the Flip-It portion angled at 45 degrees towards the subject. There are other diffuser/reflectors whic could also work.
e. Using a lens with a wide maximum aperture could be a two-edged sword. It would allow a faster shutter speed, thus freezing action but, the wide aperture would produce a very shallow DOF. However, this might be a positive or a negative, depending on your image. In a close up shot like this, shot at f/5 the shallow DOF is no problem...
This was shot at 185mm (296mm equivalent) when the dancer stopped moving, almost imperceptibly, during her routine...