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If you notice that someone's hair got shorter, which is preferred to say:Did you had a haircut or Did you had your hair cut?

Also I'd like to know which is more suitable in this situation, got or had.
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"Did you have/get your hair cut?" is fine, as is "Did you have/get a haircut?" 'Get' is possibly slightly more informal.
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In your situation I would most naturally say:

Have you had a haircut?
Have you had your hair cut?

"Did you had a haircut?" and "Did you had your hair cut?" are both ungrammatical. To be grammatical, "had" must be changed to "have".
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Comments  
gogashDid you had have a haircut or Did you had have your hair cut?
Neither was right, so I changed them so that both are correct as shown.

I would not say the first one at all. I might say the second one.
gogashAlso I'd like to know which is more suitable in this situation, got or had get or have?
I am a little more likely to say the first of the two below, though both are fine.

Did you get a haircut? / Did you get your hair cut?

I prefer those with 'get' over those with 'have'. (AmE)

CJ
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Thanks a lot everyone.😊
Did you had a haircut or Did you had your hair cut?

Explaination:
“Did you have/get?” (a haircut) is in the interrogative past-tense form.
We normally use this form of the question when asking someone about a brief, short-term, or one-time action, occurrence, or activity that took place right before the moment the question is asked, or at least not very long before that moment.

"Have you had/got?"( a haircut) is in the interrogative present-perfect form.
We normally use this form of the question when asking someone about an extended or habitual action, occurrence, or activity that took place or has been subsisting for some time in the recent past up to the moment the question is asked, or at least not very long before that moment.

Inference:
Both are grammatically correct, however,"my haircut' /your haircut "appears odd (it looks as if you had ordered a special haircut and it was being sent to you!).

Also,
Haircut is the noun form - I am going to have a haircut today.
Hair cut : hair is the object of cut, so the words should be separated.

Did You had your hair cut

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anonymous

Did You had your hair cut

There are three errors in your sentence.