I (want) ________________ to be a doctor until I was fifteen.
The answer is “had wanted” because “want” here expressed a “wish - I used to want to be a doctor before I was fifteen”. Am I correct? Thanks. Is “wanted” OK?

2. He (live) ________________ in Durban for a year before he got married.
The answer is “had lived?” not “lived – simple past?” Am I correct? Thanks.

3. I (have) ________________ trouble sleeping all last week.
The answer is “had” not “have had” because this sentence refers to the past only. Am I correct? Thanks.
1) wanted - No need to use "had wanted" unless there is a context that requires it.
2) lived, had lived - Both are acceptable.

3) had - The period of time "last week" is all in the past.

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Tha nks for your kindness. Please forgive me for being absent so long. It's a long time since I last surfed the web.
The answer is “had wanted”

The answer is “had lived?

Both of the above answers are correct. Please review the other thread about "living in Ireland before moving to London..." which I have replied.