I get canker sores after eating chocolate. Is it possible that I am allergic to chocolate?

Yes, possible. Allergic reactions are most known to be of immediate nature, most dangerous because they can cause anaphylaxis with respiratory involvement. Less known are other types of 'allergies', which might produce inflammation of skin, lip, mucosas or other parts upon contact. Elimination diets with supervised challenge is one way to find out, traditional allergy testing might be negative.
Not likely. Food allergies tend to present like other allergies, with hives and anaphylaxis, not canker sores, which most frequently are caused by physical trauma (toothbrush, self bite, hard/sharp foods). There may also be a link to citrus fruits &/or vitamin deficiencies.
Yes. In some cases that is a possibility. I would confirm with an allergist.
No. Canker sores are not a sign of an allergy, however you may be sensitive to an ingredient in the chocolate. Preservatives, especially sls or sodium lauryl sulfate have been shown to increase the occurrence of canker sores in sensitive individuals.