I think the closest that comes to your list is the Sony HX5. But I'd be very surprised if it will actually be able to take good low-light photos of moving subjects. A small camera has a small imaging sensor, and that makes it difficult for it to capture enough light. There are small cameras with slightly bigger sensors and also brighter lenses, but none will have a very long lens.
I would like to replace my current camera. I know I want a compact camera. I will be using it for child action photos at sporting events (fast action), dance recital pics (very low/no light), general photo use, video (HD), photo/video upload & print. I want better than 9 mpixels, 10x opt zoom, IS, Autofocus, HD & stero. I need connectivity to laptop and/or HDMI. I would like input on which models will fit these. There are so many that have some of this and some of that. I want one with it all. Budget is under $500.