Which digestive disease causes excessive sweating and severe burning in the feet?

Difficult to say. digestive diseases tend to cause diminished absorption of Important vitamins-minerals. It is usually the deficiency of these things that will cause the signs and symptoms. Certain states like Ulcerative Colitis or Crohns are autoimmune. Severe gastritis and ulcers can also cause severe sweating. The burning in feet gels more with vitamin deficiency like B12/folate. B6 excess can cause issues too.