User Manual Sony HDR-CX330 Digital HD Video Camera Recorder

No this camcorder does not have night shooting capabilities. It does very well in low light conditions though. I have recorded street scenes very successfully with nothing more than the street lights themselves.

THE BATTERY CHARGES THROUGH THE CAMERA.
you can get an optional charger for the battery.

The expected recording time of movies when saving on a memory card is shown as follows:
60p Quality (*)/50p Quality
Dual Video REC is set to Off: 1 h 15 min (1 h 15 min)
Highest Quality :
Dual Video REC is set to On: 1 h 15 min (1 h 15 min)
Dual Video REC is set to Off: 1 h 30 min (1 h 30 min)
High Quality :
Dual Video REC is set to On: 1 h 40 min (1 h 40 min)
Dual Video REC is set to Off: 2 h (2 h)
Standard :
Dual Video REC is set to On: 2 h 40 min (2 h 10 min)
Dual Video REC is set to Off: 3 h 35 min (2 h 45 min)
Long Time :
Dual Video REC is set to On: 3 h 55 min (3 h 25 min)
Dual Video REC is set to Off: 6 h 20 min (5 h 10 min)
32 GB
60p Quality (*)/50p Quality
Dual Video REC is set to Off: 2 h 30 min (2 h 30 min)
Highest Quality :
Dual Video REC is set to On: 2 h 35 min (2 h 35 min)
Dual Video REC is set to Off: 3 h (3 h)
High Quality :
Dual Video REC is set to On: 3 h 25 min (3 h 25 min)
Dual Video REC is set to Off: 4 h 5 min (4 h 5 min)
Standard :
Dual Video REC is set to On: 5 h 25 min (4 h 20 min)
Dual Video REC is set to Off: 7 h 20 min (5 h 30 min)
Long Time :
Dual Video REC is set to On: 7 h 55 min (7 h)
Dual Video REC is set to Off: 12 h 50 min (10 h 30 min)
64 GB
60p Quality (*)/50p Quality
Dual Video REC is set to Off: 5 h 5 min (5 h 5 min)
Highest Quality :
Dual Video REC is set to On: 5 h 15 min (5 h 15 min)
Dual Video REC is set to Off: 6 h (6 h)
High Quality :
Dual Video REC is set to On: 6 h 55 min (6 h 55 min)
Dual Video REC is set to Off: 8 h 15 min (8 h 15 min)
Standard :
Dual Video REC is set to On: 10 h 55 min (8 h 50 min)
Dual Video REC is set to Off: 14 h 40 min (11 h 5 min)
Long Time :
Dual Video REC is set to On: 15 h 55 min (14 h 5 min)
Dual Video REC is set to Off: 25 h 45 min (21 h)

Yes, you may turn off Optical Steady Shot/ Image Stabilization on your camcorder.

Face Detection with voice enhancement and noise reduction
Sony's Face Detection technology can automatically distinguish between children and adults. Face Detection technology detects up to eight individual faces and adjusts flash, focus, exposure, and white balance to help deliver crisp, properly lit images of family and friends.
it doesn't mention smiling face.