Can one learn not to panic? How? It's always impressive to listen to the professionalism of a commercial pilot communicating in a crisis situation, apparently remaining calm and in control in terrifying circumstances, with terrible responsibility. I imagine this occurs because (a) the industry does not promote those who panic to this position and (b) pilots practice a great deal in simulators, learning to cope with crisis calmly.

Am I imagining correctly, here?

To what extent can practice (b) overcome a deficiency in (a) a natural tendency to calmness?

Does practice at staying cool in one field (say, making decisions during play of a fast computer game) transfer to staying cool generally (say, being accosted by an aggressive stranger on the street)?

I read What characterises people who stay calm in crisis situations? and that does relate (a) to calmness in a crisis but I don't think it says anything about (b).
I believe that there is a fundamental flaw in your scenario in that, pilots are not promoted to being a pilot from being something else. Pilots take intensive training courses that may include simulation training and do include many hours of practice in an actual aeroplane, under supervision of a trained instructor. 

To more generally answer your question:


  Can one learn not to panic?


Yes, using behavioural training techniques we can train ourselves, or be trained by others, to respond to situations or stimuli in a different way than is our instinctive reaction. 

With the situation you noted about pilots, a trained pilot will have all of the knowledge of how to deal with a situation that they may encounter and will have practiced this knowledge in an applied setting (an actual plane) many times, making the training become the pilots first response to a dangerous situation (Exposure Therapy, and  Repetitive Learning are some ways of doing this). 

A novel situation can also be trained for. In your scenario, I would suspect that their training would include an emergency checklist type of activity that would then be repeated over and over so that it is ingrained in their memory and behaviours and will also become the pilots first response to a novel dangerous situation. 

How to learn not to panic is really all about training your brain to behave in a different way then its instincts tell it to, this may or may not mean that you totally remove the instinctive fear response.