Indoors, you’re fighting three things: low light, mixed lighting, and harsh direct flash.

To improve results:

• Use as much light as possible: open curtains, turn on lamps, and avoid very dark rooms.
• Keep to one main type of light if you can. Mixed window light + household bulbs often causes strange color. This is a white balance issue.
• Try the camera’s white balance presets instead of auto if colors look wrong.
• Use the widest aperture available and raise ISO only as much as needed. Higher ISO helps in low light but adds grain/noise.
• Keep shutter speed high enough for moving kids; if it gets too slow, motion blur will be a problem.

For flash:

• Direct built-in flash often looks harsh. A simple diffuser, like thin tissue over the flash, can soften it somewhat.
• If the flash pops up, angling a small white card to bounce light upward may give softer light, though ceiling color can affect the result.

One note: suggestions about buying a fast prime lens won’t apply to this camera, since the FZ47 has a fixed built-in lens. With a compact/superzoom, the best approach is more light, careful white balance, moderate ISO, and softening the built-in flash as much as possible.