I treat focus as a two step job at night. Find something with strong contrast that is about the same distance as your subject such as a lit sign or a bright edge and use only the center point, get focus, then recompose. Works great.
For moving subjects use AF-C with the smallest focus area your camera offers, slow down tracking sensitivity so it does not jump to the background, and choose focus priority so it does not fire out of focus. If you keep missing, raise ISO so you can use a faster shutter and reduce motion blur. Also check if your camera offers AF fine tune and run that in daytime on a target so you know the system is calibrated.
