1. Can you spare me a few minutes?

2. Can you spare a few minutes for me?
3. Can you spare a few minutes to me?

(Which one is the same as #1, #2 or #3? Which one is grammatical between #2 and #3?)

4. You will may go back home.
5. You will be allowed to go back home.
6. You will must go shopping with Ann.
7. You will have to go shopping with Ann.
8. You may have to do your homework.
9. You can have to do your homework.
10 You must be able to do your homework.

(Which expressions are correct? Which expressions are not correct? Do you have any orders in using auxiliary verbs for example: will>may>must>can)

#1 and 2 are the same. #3 is not grammatical.

#'s 5,7,8 and 10 are correct.

Will and must indicate an order.
You will brush your teeth.
You must brush your teeth.

May and can indicate permission.
You may eat an apple.
you can eat an apple.

1. Can you spare me a few minutes?

This sentence is grammatically correct.

2. Can you spare a few minutes for me?
This sentence is also grammatically correct. It has the same meaning as sentence 1.

3. Can you spare a few minutes to me?
This sentence is grammatically incorrect. The correct preposition to use in this context is "for" instead of "to". So, sentence 2 is the correct one.

Now, let's analyze the second set of sentences:

4. You will may go back home.
This sentence is grammatically incorrect. The correct construction would be "You may go back home" without the auxiliary verb "will".

5. You will be allowed to go back home.
This sentence is grammatically correct and conveys the meaning accurately. It indicates that in the future, you will have permission to go back home.

6. You will must go shopping with Ann.
This sentence is grammatically incorrect. The correct construction would be "You must go shopping with Ann" without the auxiliary verb "will".

7. You will have to go shopping with Ann.
This sentence is grammatically correct and conveys the meaning accurately. It indicates that in the future, you will be required to go shopping with Ann.

8. You may have to do your homework.
This sentence is grammatically correct. It suggests the possibility that you might need to do your homework.

9. You can have to do your homework.
This sentence is grammatically incorrect. The correct construction would be "You may have to do your homework" instead of "You can have to do your homework".

10. You must be able to do your homework.
This sentence is grammatically correct and conveys the meaning accurately. It emphasizes that it is necessary for you to have the ability to do your homework.

Regarding the order of auxiliary verbs, there is no set order in general. However, there are patterns that are commonly used. The order you mentioned (will > may > must > can) is one possible order based on the strength or certainty conveyed by each auxiliary verb. However, the context and intended meaning can influence the choice and order of auxiliary verbs used.

1. "Can you spare me a few minutes?" is grammatically correct and has the same meaning as "#1".

2. "Can you spare a few minutes for me?" is also grammatically correct and has the same meaning as "#1".
3. "Can you spare a few minutes to me?" is not grammatically correct. The correct preposition to use in this context is "for" instead of "to".

Regarding the second set of expressions:

4. "You will may go back home." is not grammatically correct. The correct form should be "You may go back home."
5. "You will be allowed to go back home." is grammatically correct and expresses the idea of permission.
6. "You will must go shopping with Ann." is not grammatically correct. The correct form should be "You must go shopping with Ann."
7. "You will have to go shopping with Ann." is grammatically correct and expresses the idea of obligation.
8. "You may have to do your homework." is grammatically correct and expresses the possibility of having to do your homework.
9. "You can have to do your homework." is not grammatically correct. The correct form should be "You may have to do your homework."
10. "You must be able to do your homework." is grammatically correct and expresses the necessity to have the ability to do your homework.

Regarding the order of auxiliary verbs, it typically follows this pattern:
must > have to > will > may/can

However, the specific order can vary depending on the context and intention of the sentence. It's important to consider the meaning being conveyed and choose the appropriate auxiliary verb accordingly.