the ski instructors are employed by the relevant ski companies and in theory they should only teach that companies tourist, however you can end up with a ski instructor from a different operator to the one you booked with - this year I will be going with Crystal but my friend is a ski instructor for Ingams so will hopefully get in their group.... basically its a free for all but in an organised chaotic way
They all one and the same. Each week they get issued with their listings. Just about every instructor will work for each and every tour company throughout the season.
They do not work specifically for one tour operator.
Only going on what my friends tell me, they say they work for Ingams and Crystal but not to worry as there will not be a problem getting me in their class if I book with Balkan or Thomson