Re: FZ1 indoors
A slave flash will work wonders. You can get a grip handle that has a hotshoe on it, mount the grip to the tripod mount of the camera, attach the flash to the grip, and set the flash to "slave" mode.
Not all flashes have a slave mode. One inexpensive one that does is the Sunpak Digital Flash (that's its actual name). It isn't too strong, but only uses 2 AA batteries and is small & light. Works fine out to 20 feet, maybe even a bit further.