Functions of Auxiliary Verbs :
As sir Henry observed, Auxiliary verbs play a vital part in making a sentence by providing if a ‘tense’ and also by making  a question.  A normal sentence has the following syntax. (Word Order)

Sub + Aux.VB+ M.VB+Object
Eg : Ravi is going out

Inorder to transform the above positive statement into a question simply placing the auxiliary verb before the subject Is Ravi going out ?

Now, let’s observe the following sentence:
‘Ravi speaks well’

For a normal spoken English learner, it’s not that easy to transform the above positive statement into a question. It is just because of the absence of the auxiliary verb. Therefore, we categories the functions of auxiliary verbs as follows:
i) They provide tense to the sentence
Eg: she is/was reading

ii) They help transforming a positive  statement  into a question

Eg : They are waiting out side.
   Are they waiting out side?

In the question/answer pattern of normal English speech, the answer need not carry the ‘element’ roused by the question.

Eg : Have you (finished your homework)
      Yes, I have (finished my homework)

Will you come tomorrow?/
Yes, I will (come tomorrow)
No, I won’t (will not)
Before dealing with the auxiliary verbs in detail, let’s know what is to be observed from them - two things.

i) Compatibility (Suitability) of the auxiliary with it’s corresponding subject.
Eg : I ‘do’ not know French

She does not know French (observe the compatibility of   ‘do/does’ with their corresponding subjects ‘I’ & ‘she’ )
ii) Representing tense of the auxiliary
Eg : is – always present tense, but in, passive construction, it represents a past action.

Eg : She is waiting outside (now) she is killed by a tiger (already action is completed)

Observe the difference:

I am invited      -         I have invited
(by my friend)     (my friend)

Many of our daily contexts demand passive construction than active construction.Observe the following:

Why have you come here?

A: ‘I’ invited (the speaker doesn’t want to disclose the name of the person who invited him. His intention is to tell that he is not an uninvited guest)

In the same way, many of the same constructions we use in our day–to–day life. Eg : I’m confused/she is questioned/ He is punished / They are admitted etc. Those who wish to improve their fluency and linguistic spontaneity, have to transform each and every sentence into the following.   

She is our classmate (Positive Statement)
She is not our classmate (Negative Statement)
Is she our classmate? (Auxiliary (or) Yes/no question)
Is she not our classmate ? ( Negative Auxiliary question)
Who is she ? (‘who’ question)
Who is not she (Negative ‘who’ question)

Note: Those who want to improve their ‘accent’ have to first come out from their MTI (Mother Tongue Influency). The best method is to make the sentences as shown above with all the auxiliary verbs or practice them by speech.

Modal Auxiliaries: The spelling is not ‘model’ by ‘modal’ which refers to the ‘mood’ of the speaker or the ‘mode’ of the action by the speaker.

Note : Although both ‘be’ forms and modals come under the same roof of auxiliary verbs, if takes a lot of shrewdness to deal with / learn modal. ‘Be’ forms are ‘safe’ in usage as each of them have a particular place to be used. Not even a learner of English language uses ‘ I’ is a student’ so ‘be’ forms do not demand a deep study but modals do.

It is not that easy for even a highly experienced English lecturer to explain the difference between ‘I will go’ and ‘I would go’ since both are grammatically correct but differ in the sense. Therefore we can broadly say that ‘be’ forms are ‘safe’ because they have a particular & one and the only allotted place for them, where as modals are highly confusing because of their dealing not with the meaning but with the sense.

Note I : Wrong usage of a ‘be’ form leads to ungrammaticality.
Note II : Wrong usage of a ‘modal leads to ambiguity (un clarity)

Personal Touch: As a English language trainer, I’d like to share one of my recent happening. I was sitting with the MD of a software company in his chamber. It was after noon 1.20. One of the software engineers had come into his chamber and said, ‘shall we go for lunch, sir, to his MD. I felt embarrassed and apologized to him saying ``oh Mr Mahesh .I am sorry, please go for lunch with them’ ( I conceived the sentence that the speaker wants the listener to come for the lunch). But to my surprise the M.D. told me that he has lunch box, but the employee want a permission to go for lunch. Here comes the problem both for Telugu as well as Hindi speaking (Indeed for Indians) because  English ‘we’ in Hindi ‘Hum’ the intention of the software employee was to get a permission from his boss for lunch. He did not have any idea to include the listener. But the very function of ‘shall’ in English is to unite both the speaker and the listener.  Eg : Shall we have a cup of tea? (you and I together). But how to make a sentence which can divide the speaker from the listener? The answer is ‘may’. Had he used ‘may we go for lunch, sir’, I’d have not been confused and kept mum, …… using ‘shall’ the speaker has damaged the primary aim of the language communication. This anecdote serves best how important it is to master ‘model auxiliaries.’

Modals :
Will : ‘willingness’ is the key not for this modal.

Shall : ‘obligation’ is the key …….
I will go there tomorrow (the speaker wants to – his willingness is to be observed)

I shall go there tomorrow (some obligation is there/he has to go / inspite of his unwillingness, he  should go)

Cliché : ‘ Cliché’ is to be largely bound in English rather than any of the Indian languages. Any  outdated expression / word grammatical rule is ‘cliché’. There is a lot for cliché to do now with ‘will & shall’. In the traditional grammar, the ‘will-shall’ rules covers an entire page. But in the models usage there is no more guarantee /  non-guarantee  for  I will come / I shall come. However as ‘shall’ shows an obligatory action, it is to be deemed that the occurrence of the action is guaranteed. Instead, the modern expression is ‘ I will come / I will have to come (obligation).

Answers for the last questions:
1. Pains 2. Dozen 3. Members of his family 4. Bad habits 5. Mob of angry students 6. Each member of … 7. Every student…… 8. Than any other Jewish Kings 9. Little 10. Many times 11. Bitterly 12. Very lonely 13. Very learned man 14. Than any of his friends. 15. Harm in trying.

Transform the following Indianism  into pure English tongue.
1. What is your good name ?
2. Save money for your children’s golden future.
3. You will find all mouth–watering recipes in this hotel.
4. What’s your age ?
5. Where is your house?
6. You only spoiled this game
7. You have spoiled your son with your own hands
8. Everyone is greedy. That’s a nacked fact.
9. The doctor is available between 10 AM to 2 PM
10. I didn’t go there yesterday why because I was ill.