What happens if the gust alleviation system on an A380 fails?
You have a few questions here so I will address them independently. But first off in a more general sense you should understand that everything on an airplane is generally designed with a failure mode this helps to ensure that if something fails it fails in a way to create the least adversity to flight. However there are event scenarios where multiple units fail in such a way that an adverse condition can be encountered. Generally (if you read accident reports) these can be avoided if an emergency landing is executed earlier on. 


  What happens if the GAS fail, if for instance two ailerons get stuck
  in an extreme position? Or maybe even worse: imagine a sensor failure
  that produces two opposite extremes on each wing, such that e.g. the
  left wing have all its ailerons in the up position, and the right wing
  ailerons in the down position.


In this case the plane still, to an extent controllable. I don't know for the Airbus, but generally speaking all systems like this have a manual override and can be disconnected. So this is implying that the system is somehow stuck on and not responding. It should be noted that in the Airbus this system does not independently actuate the flight control surfaces and most likely is bused as input to the fly by wire system. On that note a sensor failure generally does not cause extreme inputs but instead causes no input. Most things like this are at least triple redundant (so that you can figure out which sensor is bad) and if all are providing inputs that disagree the system usually disconnects and becomes inop. So to create the case you ask about you would need to have 3 independent sensors provide the same erroneous input which is highly unlikely.  


  Could this be fatal?


Its hard to say, but generally speaking no, the direct failure of a single system would not be fatal. 


  Are there procedures for this in some checklist?


More than likely but I don't have access to the official checklists so I cant say for sure.