Is a 'do' required/necessary between 'Why' and 'Burmese' in the below question statement? If yes, then why?
Why Burmese hate Rohingya muslims?
As others have observed, this could be a title (of a book, essay, article, etc), but it's not a question.
Why the Burmese hate Rohingya Muslims
The question must include the word "do":
Why do the Burmese hate Rohingya Muslims?
In English, questions are formed as follows:
When we want to ask a "why" or "how" question, we follow exactly the same rule, and then add the word "why" or "how" to the start of the sentence.
So "The house has been renovated" becomes "Has the house been renovated?", which becomes "Why has the house been renovated?".
"The boy plays in the park" becomes (via "The boy does play in the park") "Does the boy play in the park?", which becomes "Why does the boy play in the park?".
"The Burmese hate Rohingya Muslims" becomes (via "The Burmese do hate Rohingya Muslims") "Do the Burmese hate Rohingya Muslims?" - which then becomes "Why do the Burmese hate Rohingya Muslims?".
In a question, unless the question word is the subject (eg "Who is waiting?") the subject and the verb must be inverted.
In modern English, we don't invert the subject and the verb itself, but rather an auxiliary. If there is already an auxiliary, you just put the subject after it
You have eaten something. -> What have you eaten?
You can see something. -> What can you see?
You should respect others. -> Why should you respect others?
But if there is not already an auxiliary, we use "do":
He hates them -> Who does he hate? -> Why does he hate them?