The latter was really due to the faulty pitot-head design
...
The pitot tubes only stayed frozen for 60 seconds. Nobody on deck seemed to notice. Other crews have dealt with frozen pitot tubes safely.
Not a high flier but isn’t there pitot heat that can be turned on?
Yes.
If they had sat on their hands for about 50 seconds, all of the readings would have returned to normal, as the heaters and conditions overcame the icing.
However, the airplane would have remained in Alternate Law.
It will not go back to Normal Law until there is weight on the wheels, iirc.
I believe they would have been able to use the autopilot again after troubleshooting the problem per the checklist.
But did the other pilots have 2 pitots giving faulty readings at the same time? TMR can handle one bad channel, but not two at the same time.