Sorry, I had to jump in here because ballet and modern dance are practically the ONLY things I photograph! (Yeah, the fact that I'm the marketing director of a professional ballet company has something to do with that, but I was doing it a long time before that!)
The main things I want to do are tell you not to worry and to assure you that you're going to have a wonderful opportunity! The best thing you can do is put away all your preconceptions and get ready to be an alert, astute observer. A few specifics:
— The equipment you have is PERFECT for photographing a dance performance from backstage and in the wings. I can't think of a better setup than a rangefinder camera and the lenses you've got. (Technically, ‘backstage’ can mean everywhere in the working end of the theater, including dressing-room area, costume shop, etc., while the ‘wings’ are the draped areas at either side of the actual stage. Both areas offer lots of great photo opportunities.)
— Don't worry about showing what the performance looks like from the house... if people want to see that, they can buy a ticket! You're getting the opportunity to show a side of a performance that most people DON'T see. No 300mm lens required!
— Don't worry about anticipating what the company might want. Presumably, the fact that you've been granted backstage access (that's a big deal; be proud!) means they're interested in what YOU observe.
— Even though you've got permission, it's a REALLY good idea to find a few moments you can talk with the stage manager before you get started. The stage manager is the boss of everything that happens backstage. Of particular importance, s/he will be able to tell you areas that it’s important to stay out of (because of the dangers of moving scenery, flying bodies, etc.) and where you can stand without being visible from the house.
— During the performance, things move very fast backstage: dancers have to run off and make quick costume changes, people are going from one side of the stage to the other, they have to find props, emergency costume repairs need to be made, etc. This can make for exciting and authentic images, just make sure you DO NOT GET IN ANYONE'S WAY EVER! What you're doing is important, but the show is still top priority.
— Shoot a lot, because you'll have a lot of duds. Metering is going to be hard because of the varying lighting conditions you'll encounter — the stage is bright, farther back in the wings it's dark, the shop and dressing room areas are a mixed bag. When I'm in the wings I love to shoot straight into the lights and let the lens flares fall where they may, but it's almost impossible to get a meter reading that makes sense, so just take your best guess and then bracket!
A few seasons ago I shot an entire performance of “Giselle” almost entirely from the wings, and I just threw a bunch of those photos into a Flickr album in the hope that it will get you enthused about this opportunity:
https://flic.kr/s/aHsmKVYZzH
Final thought: Everything you think you know about ballet is probably wrong! Let go of your preconceptions and see what's there!