I downloaded the first photo you posted but was not able to get your EXIF nfo from it ??? Most often indoor blurryness is caused by shutter speed beig too slow... To avoid motion blur keep the shutter speed as high as you can indoors when using the flash. Film SLRs usually synch to 1/125 of a second if you want a rule of thumb.
Apart from this, don't know what else to say. I've seen some very nice indoor snaps - crystal clear, from FZ-20 users posted here. Also, your snap-shot posted doesn't look that bad to me. It's a little noisey but it's not blurry.
Also, when you post a full size 1200 X 900 (or whatever) picture, the noise and artifacts will always be highlighted, if they're there. But you're never gonna view your shot this large, and these imperfections are minimized when printed or viewed on a PC at a normal size.
As far as "not knowing anything about photography"... then blaming the camera... well, photography does require a little bit of technical knowledge. Much of the basics you can pick up - literally, in a couple hours. 2/3rds of what you need to know is probably covered in the manual. Understanding the basics - the interrelationship of shutter speed, aperture opening, and ISO speed isn't rocket science.
I don't mean to seem indelicate, but invest a little time perhaps?