I don't have one myself...but I did shoot for years with one of the forerunners of that cam, the H5. I'd expect performance to be fairly similar...but this will hold true for any ultra-zoom point&shoot camera, whether it be Panasonic, Canon, Sony, Olympus, Nikon, Fuji, Kodak, etc.:
1. Low light indoors - poor for just snapshots, better if you take the time to set up the shot with some photographic knowledge, fine if you use a tripod, low ISO, and a longer shutter speed. In general, P&S cameras won't do hand-held snapshots of low-light indoor scenes well - no matter the brand. You need more light, and just don't have it - and raising the ISO will mean more noise and more noise reduction smearing. There's got to be some compromise in a sub-$400 compact camera...and this is it!
2. Outdoor night shots - Not good if you want to do handheld snapshots...but even a basic DSLR with kit lens wouldn't be very good for that. For handheld night shots, you need seriously high ISO levels and a seriously low-light lens (F1.0-1.8 or so). Assuming you mean the more common tripod, slow-shutter night shots - you should get very good results. These cameras perform quite well at the lowest ISO, up to 30-second shutter speeds, and plenty of depth-of-field for landscape scenes and such. I took tons of night shots with my H5, and had great results.
3. Fireworks - Same as night shots - good to excellent results, if ISO is kept lower, tripods are used (or level surfaces), and of course good timing to get the fireworks bursting at just the right time.
The H-series cams are quite good - for sure they are as good or better than any other ultrazoom. It's a near-tie, honestly, with ultrazooms, with none all that much better or worse than another - be it the Panasonic FZ series, the Canon S-IS series, or the Sony H-series...or Fuji, Nikon, or Olympus' entries too. Don't worry too much on brand - go for price, features, and personal style to decide which one is right for you. None will be outstanding in low light situations unless you can set the ISO low and take nice, long exposures with the camera on a level surface or tripod, in which case they will all perform beautifully.