A. It's all right to say "good" to the question "How are you?" but not to "How are you doing?" Here's why:
In "How are you?" the verb is a linking verb. A linking verb can be followed by a predicate adjective. A predicate adjective comes after the verb, but it describes the subject. In effect the answer says, "I am good."
In "How are you doing?" the verb is an action verb. The modifier that comes after an action verb has to be an adverb, not an adjective. It has to be "well" rather than "good." To say, "I am doing good" would be incorrect because an adjective is used to modify a verb.