AutoNav is simply given a set of waypoints, which the software then has to, on its own, plan and execute a route. You can imagine the waypoints as lawn darts on the 3D terrain map built from the previous sol's images. In fact, in the rover planning tool, the waypoints are displayed as actual lawn darts.
The plan is executed about a meter at a time, heading in the direction of the waypoint as permitted by the terrain. At each step the rover will build a safety map of the terrain ahead and go around obstacles as needed. The drive can terminate before reaching the final waypoint if either no progress can be made safely, or the allotted time has been used up. Regardless of how the drive ended, images are always taken of the final state for use by the rover planners on Earth for the next sol's plan.
Yes, arm, drilling, sample movement, instrument operations, etc. can all be executed autonomously over a sol or longer. Those are generally well-specified, deterministic actions (unlike waypoint driving), and the sequence terminates if any unforseen problems are encountered. Drilling and sample movement activities are done over several sols so that the operators andon Earth can be in the loop and verify proper progress along the way.
The rovers are designed to be autonomous enough to keep themselves busy for a full sol. They normally get only one set of commands direct from Earth when they wake up in the morning, and then send back the results the sol's activities in the afternoon through a relay orbiter, before going to sleep.