Does food cause rashes on body and face?

Possibly. Food allergies may cause hives (urticaria). In some individuals with eczema (atopic dermatitis), food allergy may make eczema worse. Also, patients with celiac disease (gluten sensitivity) may develop a rash (dermatitis herpetiformis). For those people with true food allergy (ige-mediated), every time they eat the offending food, they have reproducible symptoms within a short time period.
Absolutely. Sorting out food allergies can be tough. Both serologic and skin testing can be done.