Generally speaking (not specific to Airbus), what the layman refers to as "autopilot" is actually three logical systems:
The Flight Management System (FMS), which figures out where the plane is in relation to the supplied flight plan.
The Flight Director (FD), which figures out how to navigate the plane to where the FMS wants it or according to manual ...
Since you tagged airbus, I will answer for the A320. The following image from the FCOM shows the FCU (Flight Control Unit) on the glareshield:
This is where all inputs for the autopilot are made. The second knob is the HDG OR TRK SELECTOR KNOB, which allows setting a heading. In general these knobs work as follows:
To make the autopilot follow the flight ...
As @Bianfable points out in the comments RVSM airspace is a problem but ignoring that for a minute:
The question of will they continue? depends on the airlines op-specs. Different airlines will handle this differently and it may very well be handled different on different airframes within an airline. A call to base may even occur but there are lots of ...
Moving the flight controls above a certain threshold will disconnect the autopilot.
From the A320 FCOM (1.22.30 Auto Flight - Flight Guidance, emphasis mine):
AP1 or 2 disengages when:
The pilot presses the takeover pushbutton on the sidestick.
The pilot presses the corresponding AP pushbutton on the FCU.
The pilot ...
When autopilot is engaged the pilot can't override the commands. If the autopilot senses manual forces on the controls (sidestick, rudders, ths) then it disengages.
Alternate law has nothing to do with the autopilot rather the flight by wire system. In alternate law there are less protection (like alpha-floor and others).
I don't know if the autopilot ...