Be aware that the features you are asking for are at odds with each other, so you will probably not find the perfect camera that checks off all your boxes.
You're looking for a small point-and-shoot class camera to take to concerts and sporting events, but you want 30x zoom and good low-light shooting. Presumably you will attempt to shoot these photos handheld, since you've mentioned the "stealth" factor and these venues would probably frown upon bringing in a tripod.
A strong zoom is at odds with good low-light ability since you will need lots of light to overcome both the optics of the zoom lens and the fast shutter speeds necessary to take a photo handheld. Yes, image stabilizers help, but they only do so much. There is a reason why most sports photos are taken by pro photographers with gigantic lenses on their cameras.
The Sony HX50V looks decent from a quick look at specs. Personally I second the recommendations of the Canon Powershot S110 and the Sony RX100. The RX100 in particular has a comparatively HUGE sensor which translates directly into better low-light sensitivity. These two cameras are also extremely responsive (the RX100's burst mode is astonishingly fast) which is good for sports.
Shutter speed and ISO (sensitivity of the sensor) affect your ability to take photos in varying light conditions. For low light shooting, you want the ability to take a clean image at high ISO, so you can shoot at a shutter speed that's not so slow as to make everything look blurry. For sports in plenty of light (outdoor stadium on a sunny day) you want the ability to shoot at a fast shutter speed so you can get sharp photos of fast-moving players.
AVCHD video is indeed editable by iMovie and Final Cut Pro.
If you are truly looking for a high-sensitivity long-zoom camera, but are actively avoiding the DSLR form factor due to size/weight/"pro look" constraints, you may want to up your budget to consider interchangeable-lens cameras such as the Sony NEX series or micro four thirds (Olympus, Panasonic).
