mm43;
The > 10 second disagreement is the trigger for ALTN 2, and it seems that the NAV ADR DISAGREE would remain for rest of the flight.
Yes, and for ALTN 1 as well. This change was made around 1997. Prior to this change, a momentary loss of valid air data would latch the EFCS in ALTN law for the balance of the flight. As far as I can determine, the only conditions which would cause the loss of AP 1 + 2 for the balance of the flight are the NAV ADR FAULT 1(2) + 2(3):
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The only other possibility (only because it isn't clear if the AP is lost until landing) is the Abnormal Attitude Law, which if set pitch and/or bank angle values are exceeded, the laws revert to, in roll - yaw alternate, and in pitch - an adapted Nz law, without autotrim.
The autopilot will not engage without autotrim, (Use Manual Trim). After aircraft recovery, and until landing, the laws stay the same for roll but revert to Nz law with a recovered autotrim. I would expect the autopilot could be engaged depending upon other factors, (both elevators controllable, yaw damper functioning).