Not on Boeing and Airbus aircraft. The AOA is measured by the angle air flow sensor or also called angle of attack probe.
Beside the AOA probe data, laser gyroscopes also provide data to the ADIRU's. There are two AOA probes, one on each side of the forward fuselage. On the A330, the pilot AOA probe is connected to ADIRU 1 while the first officer AOA probe is connetced to ADIRU 2 (while ADIRU 3 is not connected to any AOA probe).
I know one case (but it was the static port, not the pitot tube). There might be a few more but certainly not "uncountable". Also, clogged pitot static systems are a general issue in aviation, not only for heavy Boeing aircraft.
Yes, but still the AOA can only be accurately measured by dynamic pressure sensors. A pure inertial reference system, which can drift by up to 0.32° over a 16h flight is pretty inaccurate, when the range of practically legal AOAs is between -1° and +5°.
The pure inertial calculation would be used, when both air data probe measured values are considered wrong. This could, when your description of the A330 air data system is correct, already happen when one Air data probe is clogged and the inertial reference of the third unit being closer to the wrong air data probe (with the intact air data probe being considered the erroneous reading)
First it rules out the intact probe and flags it as damaged, as the damaged air data probe is closer to the inertial measurement.
Now, you just have to make sure, that the pure inertial reference is flagged faulty. That both air data probes at the same time fail and you have to use inertial can also happen, but the inertial is then rarely wrong by about 10°.
Re automatic speed/stall protections, there is a whole class of safety measures that could be considered detrimental to normal operations due to false positives. Another example demonstrated at the Motor Show here recently - automatic safety brakes on vehicles. What if this system malfunctions on the Autobahn and you end up with a end up with another car plowing into the back of you at 200km/h? It is hard to say whether these systems are good or bad overall.
Well, I am from the mind set closer to the Airbus doctrine of letting the aircraft control it's limits itself, with the pilot being able to override (with a single press of a red button on his stick BTW).
On your car example: An emergency braking from 200 km/h would be annoying, but not deadly. When somebody plowed into your back then, it is his fault of violating road traffic laws (safety distance and/or medical state and/or technical safety). You can't blame the emergency brake on your car then, but rather the lack of one on the other car.
But still, if your car has an override button to allow you to abort the automatic emergency brake, you would have enough time to react. For the same reason, with our natural distrust of technology, all cars I know allow disabling the ESC, even though the system is meant for increasing safety. But especially early version of can be worse in extreme situations.
It is like the cruise control switch. If you know what it does and what it's limitations are, you are a good driver. If you enable it and go to the back of the caravan to make a coffee, you are a very very bad driver.