Does a prolonged elimination diet (eg aip) cause food allergies or anaphylaxis to foods that you eliminated?

Not usually: If you eliminated a food you are allergic to even for a long time, the reaction is unpredictable on reintroduction but it is unlikely that this action alone eliminates the food allergy. However some food allergies do tend to fade away (milk, egg etc0 with time-whether this is from having avoided it for a long time or not is unclear.