Can we say same colour that is ongoing in game after keeping wild card of change colour? As in if the round was of red my brother kept wild card and said the colour will stay red so that he can discard his red card and win .... is it correct way ? As I felt change of colour should have happened?
According to the official rules found via a google search 'uno rules' (emphasis mine):
Wild Card - When you play this card, you may change the color being played to any color (including the current color).
This means that when you play a Wild Card you can name the current color.
First of all, you don't have a turn after using a wild card.
Second, Your brother didn't violate any rules. If the going color is red and he used the wild card to keep the color to red only- there's no fault in that.