The "superfine" setting is only controlling how much compression you want applied to JPEG files (trading off gradations between colors against file size). Noise comes from underexposure and high ISO settings.
Cameras need more light to see by than your eyes do. Shooting indoors at low light, any 1/2.3" format sensor (like the one your camera uses) is going to exhibit noise. And then zooming in to see individual pixels will make that noise more apparent than they would be at the image level.
If you want to improve the image quality indoors in low light, and you're shooting a stationary subject, you can use a tripod and timer (so you don't shake the camera during the exposure), and use a longer shutter speed with a lower ISO setting. If you're shooting a moving subject, then adding flash or some other form of light to the scene is your only recourse. You might also try using some form of post production to do noise reduction.
Superzoom bridge cameras, like the Canon Powershot SX series, trade off low-light performance for reach. The longer the lens can reach, the faster your shutter speed needs to be to avoid camera shake blur, and the smaller the maximum aperture (how wide the lens opening can go) will get. For low light, you typically need a lens with 5x zoom or less, and the bigger the sensor the better. That's why, at the other end of the spectrum, there are large-sensored compacts like the Fuji X100S, which have APS-C sized sensors like dSLRs, and fixed lenses that don't zoom at all.