Ok let's get to the point-
there is an assumption here that British people hate Indians/ Asians
what is all this about?
I am not sure Simon (about American "big city" accents). I know that in Chicago there was a huge amount of German immigrants that started in the 1870's and petered off a long time after (I do not know when). And then in cities like New York City, Philadelphia, Pittsburgh, Los Angeles, San Francisco, there is a mixture of almost everything you can imagine. SOme cities have been know for a particular group, but on the whole there is a lot of diversity. For example, the Chinese in San Francisco, the Italians and Irish in Boston and the Mexicans in Los Angeles.
And the area of New York and Vicinity, there is an accent that would be the closest American equivalent to British English there is, but I do not know why this is.
Were the 13 colonies actually called the United States before they became independent, or were they just known as British colonies?
Methinks your question is based on a false supposition.
There were 13 colonies. It was not a single territory. They had different statuses and relationships to the Crown and to one another. And most started off as English, with Great Britain being formed later.
My guess is that in Mother England we referred to them as the American Colonies when speaking generally or maybe the Thirteen Colonies. Their individual names would have been used a lot I think, such as Virginia, Georgia, Maryland etc.
In fact maybe they were referred to as the The Thirteen Colonies of America, and United States of America as a name borrowed the same pattern but this is pure speculation.