Well, freezing action means fast apertures.
Stage dramas are not that bad, as the actors don't move as fast as athletes, but the lighting could be dull. It doesn't help that they usually have black backgrounds.
Also, with a long lens like a 70-200/2.8, shake becomes import in low light and low shutter speeds. Depending on your position, you could use a lower FL. Or maybe a monopod/tripod?
Try to use center-weighted or spot metering, but for spot, you need to be able to pick the right spots.
50/1.7 or 1.4 or 85/1.4 are good, but primes are limiting as you can't always keep moving to zoom in or out.
Zooms limit you to 2.8 or slower. So you need a good body that can handle high ISO's. What body do you use?
Also, shoot in RAW. That way it's easier to boost the exposure compared to jpegs. WB won't be much of a problem either.