Which one is correct way of asking Questions ? When to ask questions without auxiliary? Is asking question without Auxiliary is more formal way of asking questions ?
a) Are you Ok? b) You ok ?
a) Did you see that movie? b) You saw that movie ?
a) When did you see that movie ? b) When you saw that movie ?
a) Who did give you this? b ) Who gave you this ?
When forming a question in English, there is what is "correct" and what is more or less formal. Firstly, you should review how questions are normally formed in English, because there are several different types.
Dropping the auxiliary verb or using statement order instead of question order is sometimes done in informal speech, but it's more complicated than that.
a) Are you Ok? b) You ok ?
In this case, a) is correct and formal, and b) is correct in informal speech.
a) Did you see that movie? b) You saw that movie ?
As with your first example, a) is correct and formal, and b) is correct in informal speech. It's an example of using statement word order as a question.
a) When did you see that movie ? b) When you saw that movie ?
In this case, though, a) is correct and formal, and b) is never correct (except in some dialects). When asking a when-question, we always use an auxiliary verb if there is another verb in the sentence: When was the festival? but When do you eat? When will they arrive? When did she write her book?
a) Who did give you this? b ) Who gave you this ?
Here, a) is only correct as an example of the emphatic do, and b) is the normal question form. You would only use a) in a case like
Did Mike give you this? No? Well then, who did give you this?
Your first example doesn't contain an auxiliary verb at all. Auxiliary verbs are verbs that are used along with a main verb to form a question. In the first example, the conjugated verb "are" is the main verb. It is not an auxiliary and can't be omitted. (However, in casual spoken English, it is acceptable to omit the verb entirely in some situations like this one. This would usually not be done in writing though.)
In your second example, both versions are acceptable, but have slightly different meanings. "You saw that movie?" implicitly expects or assumes an affirmative answer. "Did you see that movie?" carries no such expectation.
In your third example, only the first case is grammatical. "When you saw that movie?" is ungrammatical in both spoken and written English.
In the last example, the second case is what you want. The first case, "Who did give you this?", puts the auxiliary verb in an unusual (but grammatical) place. In this position it serves to emphasize "give". It emphasizes that you are asking who did give the item rather than who did not give the item.
