Do food allergies go away if keep eating same food over and over in small amount?

Not exactly. Be careful. There are currently no fda-approved protocols for oral desensitization to any food. This is still an experimental topic and I would not suggest that you attempt such a procedure.
Do not try. If this is a true food allergy you can make matters worse and not better by repeatedly challenging the body with food proteins. Protocols for food desensitization are currently being developed to be performed under the supervision of a clinician and should not be attempted until the have been approved and verified.
Depends. There are many types of food allergies. It would be dangerous to try giving small amounts of food if you have a classic food allergy (hives and anaphylaxis). The exception is milk and egg allergy: if you can eat "baked" milk and egg (e.g. Muffin or waffle) without a problem, this can help you tolerate regular milk and egg over time. It is best to discuss this with a trained allergy specialist.
No. Repeatedly stimulating the immune system with small amounts of food just keeps the reactivity going, unless it's done under an allergist's supervision as a desensitization diet. Most children outgrow food allergies (except peanut and shrimp) by strictly eliminating them from the diet for 2-5 years. Adults still allergic to foods are typically stuck with their food allergies for life.
Unfortunately, no. If you have a true food allergy (not just intolerance) & you keep eating the allergenic foods, you'll stay allergic to them (the rare exception would be doing desensitization while supervised by an allergist). Kids may outgrow some of their food allergies if they avoid those foods for a few years, but most adults are stuck with their food allergies permanently. Your doctor can help you with this.
Possibly. It is like desensitizing if you start very slowly with small amounts and prepress slowly. It is like allergy shots for desensitization.