1) when reliable airspeed information was recovered, did the flight control system switch back to normal mode with all the protections available or not? (I presume not). Is this by design?
No and yes.
2) would some kind of automated high altitude stall recovery be conceivable on such a plane? at least forcing a stick push action?
If you trust a computer (and the data it's fed with) enough to do an automatic recovery you could just as well let it take action before the actual stall occurs. Then you have what an Airbus gives you in normal law.
There are devices like stick shakers (literally rattling the yoke to alert the pilot by other means than just the aural stall warning) and stick pushers (required on some a/c with unfavourable stall characteristics, automatically pushing the controls ND to initiate recovery). Both systems help but are no sure fire solution. There have been incidents where the action of the stick shaker has been mistaken for mach buffet (a sign of the aircraft being too fast) thus provoking exactly the wrong actions. Even stick pushers have been overridden right into the ground. As they say, invent something foolproof and nature will come up with a better fool.