The camera is equipped to capture any kind of moment or particular lighting situation. You need to find the right settings to use, You also need to know how and what needs to be adjusted for your situations. Your question, " How good is the auto focus system, in low light situations" i just bought an alpha 37 and managed to produce some awesome photos using the "no flash intelligent mode" the artificial intelligence built into the camera is designed to respond and focus, now the speed of a focal point depends on how much money u want to spend ... a higher priced camera most likely in the thousands of dollars is equipped to have intelligence move at extremely fast speed. I bought the alpha 37 because i am not going to walk on water hypothetically speaking. if you want to walk on water i would recommend spending money on a higher quality camera...
with that out of the way i having been using the artificial intelligent mode: which this camera offers a few modes : flash off intelligence flash on intelligence +flash on super intelligence mode panoramic mode 3d mode there is other modes too but i haven't had enough time to educate myself on all of the modes.
i personally would use the super intelligence with the flash on . on the camera its the intelligence + mode, in this mode you you just point and shoot. but a lot happens behind the scenes.
The auto focus system is great i had no problems i recently switched my modes from inteli-flash-off to inteli-flash-on-super. now we have to discuss the flash of the camera during a corrupt lighting situation... i got some photos wtih movement in the scene and the camera automatically turns on the flash which then bleaches the entire photo with color white.
i prefer natural light, who doesn't, i find the flash in the camera makes things look almost artificial so i try not use the flash ever unless i need an alternative light-source.
your question, " How good is the auto focus system, in low light situations" and "will it capture a child moving in low lighting situations"
1. i had no problems with the auto focus system in low light situations. (got some incredible photos with in the low light moments)
2. now, a moving object is a different story u need to capture a moving figure . this is what i would do it on my alpha 37 : switch modes to superior intelligent mode the flash will kick in because its picking up low light... in this mode u can capture fast moving "nouns"(person place or thing) but the only thing is going to get in your way, is the built in camera flash. it will bleach out the photo. getting rid of all natural light and use the artificial light. we don't want that we love natural light. making the light look artificial is a bad thing. unless you want that artificial behavior. using natural indoor light should capture the mood and tone that is in the room at that time.
lets be blunt for a moment... to answer your question "yes the camera is great for capturing low light situations and great at finding the focus of your subject but in motion i haven't actually tested it out yet i am going to do that now ... if you want my email so i can send u some pictures that i took if u want to see how the camera reacts to each situation.. email@example.com
the view finder on this alpha 37 is wonderful i bought this camera because of the view finder... it automatically scans your retina knowing when and where your eye is... i thought i was at the eye doctors taking a test, while configuring the view finder for my eye....
there are so many better cameras out there. do your research. find something that u can relate to. i related instantly to the alpha 37 when i saw how the view finder works. and of course i had only 500 dollars to spend for a camera. so for 500 dollars i choose alpha 37
I tried using the tracking focus feature and set it on my cat in a dark hallway, it tracked her until she got in the light and then it got confused. Overall, the focus tracking seems so-so, probably better in higher light situations. Focusing normally with a half press of the shutter button yielded acceptable results however, so I don't think I'd count it out, but I feel that focus tracking might be more of a gimmick.