Maintenance requirements are specified in the manufacturer's Instruction for Continued Airworthiness. The POH/Flight manual will have a supplement that gives limitations & procedures for use. There is nearly always some form of pre-takeoff check that the AP is functioning correctly.
The POH supplement will specify what approaches the autopilot is approved to do.
Common GA autopilots (ignoring wing levellers) are 2 axis (roll & pitch) + heading hold. Those types don't coordinate turns. Others are 3 axis, sometimes via a yaw damper, and can be able to keep the turn balanced, or near nearly balanced.