Indoor action photography without flash can be a challenge. You will need a camera that handles high ISO well and a fast lens. Here I’ve used a Canon 5D Mark II with a 24-70 f/2.8L.
To freeze action, use a fast shutter speed. This means higher ISO and wide aperture. Higher ISO will result in more noise. It’s not necessarily a problem if your photos are for small format and screen only.
You don’t always have to reveal everything. Leave something to the viewer’s imagination.