where were you born.?

Tenses have no bearing on whether speech is direct or indirect. Quotes are what make it direct. Consider these:

Direct Speech

"Where are you living?" he asked. -- Present

"What will you be doing in Chicago?" he asked. -- Future

"Where were you educated?" she inquired. -- Past

Indirect Speech

"He wanted to know where I attended high school." -- Past

"They asked where I would be living if accepted into the school." -- Future

"She asked which doctor I am seeing." -- Present

Btw, even the asking of the question can be in another tense:

Direct

He asks, "Where were you born?"

Indirect

"He asks where I was born."

Indirect (but in future tense)

"He will ask where I was born."

"I was born" is Simple Past, and you generally only every use the Simple Past when stating the place of your birth or to whom you were born. This is because you are born once and only once, and the event occurred during a clearly defined span of time. The only other time one would deviate from the Simple Past is if one said "I have been being born." OR "I am being born." These are the Continuous Present Perfect and Continuous Present, respectively. You would use the Continuous in creative writing.

You cannot work all language rules out with logic and pattern, because that is not the way language works, certainly not English, which has many MANY parent languages -- languages that influenced it and/or added to its vocabulary.

The past perfect expresses the idea that something occurred before another action in the past. It can also show that something happened before a specific time in the past. Because you're not comparing 2 or more events, the simple past, especially with the verb "to be born," is the tense you want.

In the US, "where I was born" is right. It would never be "where I had been born".

I think the same is true in the UK because in general the rules of grammar are the same, but sometimes there are small differences so I'm not absolutely sure.

No, the sentences are right.