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A: What else do I need to know about my personal identity?
B: Well, you know your date of birth, when you were born.
Now you need to know your place of birth, where you were born.
A: I know that, I was born here, this place, your workshop.
B: That’s right.
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where you were born.
Is it an interrogative sentence?
Does it mean “it means where you were born.”
**
when you were born.
Is it an interrogative sentence?
Does it mean “it means when you were born.”
Thank you
They are both declarative statements. The part after the comma is rephrasing the first statement.
“You know your date of birth.” - Declarative Statement.
“… when you were born.” - This rephrases the first statement to add more clarity.
The sentence about place of birth does the same thing - it rephrases the statement.
A declarative statement can usually be turned into an interrogative sentence by a slight rewording, or change in the tone of voice.
When written, sometimes the only thing that’s needed to turn it into an interrogative sentence is a question mark. When spoken, the only difference might be tone of voice. So the exact same words might be either a question or statement.
A: You know your birth date. - Declarative
B: You mean when I was born. - B rephrases it as a statement.
B: You mean when I was born? - This is a question.
or
B: [Do] you mean when I was born?
The word ‘do’ is often omitted. So “You mean when I was born . / ?” can be either a statement or question.
When spoken, the declarative statement tends to be said in a flat tone of voice. The questions tends to raise in pitch.
Thank you so much, NearlyNapping 
Very nice explanation.
It is not an interrogative sentence. Syntactically, it is a dependent clause.
In order to make a question, you need to bear in mind that the verb-subject order is necessary unlike the usual subject-verb order for assertive and other types of sentences.
Accordingly, When were you born? will be a grammatically acceptable interrogative sentence.
Thank you so much, Anglophile
Very nice.