Yes. Food intolerance or allergy can definitely cause irritability in an infant. However, an irritable infant should be examined to rule other or more serious explanations.
Yes. Food intolerance can cause increased gas production in the bowel resulting in irritability. The most common example is lactose intolerance. Certain foods can cause more acid reflux and discomfort. Food intolerance is different than food allergy.
Yes. A baby can be more irritable if he has intolerance of particular foods, because he may get some nausea, spitting, tummy aches, gassiness, diarrhea, and/or constipation.