You will need following things

1. A DSLR camera with a 200mm+ telephoto lens or a point and shoot camera that has an optical zoom capability.
2. A stable tripod.
3. Remote camera trigger (optional). If you do not have one, a timer in your camera will also work
4. Make sure you are in such a place where city lights don't affect your photo shoot. I would suggest going outside city area where you can find no lights, like Highways, Village etc. 

And following camera setting

Camera Mode: Set your camera mode to full Manual Mode.

ISO: Set your ISO to 100. If you have a point and shoot camera, see if you can find a menu setting to set your ISO to 100. Make sure “Auto ISO” is turned Off.

Aperture: Set your aperture to f/11.

Shutter Speed: Set your shutter speed to 1/125 

Lens Focus: Set your lens to manual focus (either through a switch on the lens or on the camera) and set your focus to infinity. Be careful while setting the focus to infinity, as some lenses allow focusing beyond infinity. If you do not have such a feature in your camera, then try setting your lens to the center of the infinity sign, then take a picture and see if it came out sharp by zooming in the rear LCD of the camera.

And voila, you will get this type of results

http://nisargpandya.com/portfolio/different-moods-of-moon/

1. Shooting with 50mm lens can let you shoot at aperture as wide as 1.8 but a 18-55mm will allow you to shoot only at 5.0 aperture 
2. This difference itself is a huge deal. This means you can have the advantage of having faster shutter . Imagine shooting handheld at 1/15s with aperture f5.0 and then at 1/125s with aperture f1.8. This can be significant in low light conditions.

It depends on where are you uploading your pictures. Irrespective of the place, you watermark must be small enough not to cover much of your photo. You can keep your watermark mostly around bottom corner.  

First of all that you should not try to disturb the audience. Always try to capture pictures from roaming around the walls of auditorium. Better to go with Telephoto for taking candid shots for stage subjects or from the audience.

Another thing is that you can use another camera for wide angle shots of entire stage or the audience.