The following are answers to Abdulla's questions:
Q 1) What is the difference between "auxiliary verbs" and "linking verbs"?
Auxiliary verbs are also known as helping verbs. The verbs Be, do, Have, and Modals, (such as Can, Shall, Might, Could,..etc) are auxiliary or helping verbs. Auxiliary verbs or helping verbs are used in conjunction or combined with other main verbs in a sentence or clause.
"I am writing a research."
In the example, above the auxiliary verb(be / am) is a helping verb that occurs in conjunction or combined with another verb (the verb Write + ing). So, the auxiliary verb (am)in this sentence helps to express the progressive or continuous aspect of the main verb or action in this sentence.
Example 2: "I am a lifelong learner."
a linking verb is a verb that links a noun, or an adjective, or both nouns and adjective with their subjects. In the example, above the verb be (am) is a linking verb since it links the noun (learner) and the adjective (lifelong) with their subject (I). Also, a linking verb, such as verb be can be replaced with the symbol (=) And the sentence would still make sense. For example, I = lifelong learner.
Please note, the verb be can act either as auxiliary or as a linking verb. For more details on Linking Verbs, please visit: http://grammar.uoregon.edu/verbs/linking.html
2) What does "intransitive verb" mean?
A transitive verb is an action verb that takes a direct object; for example, the child broke the window; (broke) is a transitive verb because it has the direct object (window). In other words, the action of breaking occurred to the (window). For more deitails on transitive verbs, please visit: http://grammar.uoregon.edu/verbs/transitive.html
Hope this helps!
PS Please let me know should you need more help with these topics.