While “touch” is not as common as a linking (intransitive) verb as it is an action (transitive) verb, it can be grammatically categorized as such. If you express “I touch” as a general statement of ability without a focus on anything particular being touched, “touch” would be a linking verb in that context.

No, they are not the same. This post explains what a linking verb is. Please see our post Helping Verbs: Examples of Helping Verbs for information on helping verbs.

In American English, we have typically always referred to “linking verb”; “copular verb” is seldom if ever used as a reference for a verb that links a subject to a subject complement. If “copular verb” was used in rare instances decades ago, it has since faded from the mainstream.

No, the verb has is not a linking verb. Because the verb has can take a direct object (e.g., long hair), it is categorized as a transitive verb. For more information, you can refer to our post Taking Charge of Transitive and Intransitive Verbs.