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What can I do to reduce the noise in pictures like this? Also, what is

missing? Angle? Spacing? Any help is appreciated.

It depends on just what settings are available on your camera (I'm not all that familiar with the DSC-H50). You can also reduce noise using Photoshop with various denoising filters, provided you're willing to accept a slightly less sharp image. On the camera, you can try reducing the sensitivity (ISO setting) -- lower ISO settings generate images with less noise on almost any sensor. You could also try to take steps to either darken the background or throw it out of focus. Either way would help bring up your subject. You have a relatively limited aperture range, but you could try either increasing shutter speed, or just stepping back and using more zoom. This would also help diffuse the flash a bit.

I suggest turning the sharpening function off on camera. Then sharpen selectively, not sharpening the background at all in whatever program you use (e.g. photoshop). That way you don't sharpen and therefore emphasize any noise in the dark background.

...about the noise - I have the same issue in darker photos and have been told that I need a better lens (with lower F-stop).

 

As for the composition, it needs work. Assuming you couldn't get the model to face the camera, perhaps framing the image so the emptiness is in front of her would have added to the impact....sort of a "despair in the face of hopelessness" approach.