which sentence is correct?
1. Does the Christmas holiday begin?
2. Is the Chirstmas holiday began?

Question

which sentence is correct?
1. Does the Christmas holiday begin?
2. Is the Chirstmas holiday began?

Answer

"Does the Christmas holiday begin?" You need a time here. Now? Tomorrow? Next week?

The other problem is that it is not one day which is the Christmas holiday, but maybe a week or more. So treat it as a plural: "Do the Christmas holidays begin this Friday?"

"Is the Christmas holiday began?" has a big problem: "is"=present tense, "began"=past tense.  Your best options are: "Did the Christmas holiday begin?" or even better, "Has the Christmas holiday begun?"  Again, better to use a plural.

"Have the Christmas holidays begun?" makes most sense, because the 'have ...begun' pattern (present perfect) means the beginning of the Christmas holidays is important now.

Answer

1. is grammatically correct.

The question was elementary dear. I suggest revising some of your very first lessons.

Answer

"Does the Christmas holiday begin?" is grammatically correct but probably isn't what you meant.  This sounds like "Does the Christmas holiday have a beginning," which it does, so the answer would always be "yes," regardless of the time of year.

"Has the Christmas holiday began already?" is grammatically incorrect because the past participle of "to begin" is "begun" not "began."  It should be "Has the Christmas holiday begun already?"

Answer

It could be
1.When does the Christmas holiday begin? or
   Does the Christmas holiday begin *in December?
2.Has the Christmas holiday began already?

Answer

Neither are correct, if you put them in a context maybe... the question can be formulated : 
    When does the Christmas holiday begin ? 
you have to add When an adverb of time  ( refering to time ), you usually have to add adverbs like when , waht , how , which , whom if you want to ask something