Are neurological disorders commonly associated with celiac?

Possibly. Celiac disease can be associates with peripheral neuropathy or ataxia. In some cases these syptoms become apparent before celiac disease is diagnosed.
Not often. Celiac disease involves intolerance to glutens with lots of GI symptoms. Vitamin and other nutrient deficiencies may develop. In children some concern has been raised about learning and behavior defects due to the disorder. Early diet management seems to help. Blood tests can diagnose the disorder. Pediatricians are trained to monitor development and to monitor nutrition.