It depends on what type of hair coulour you have. If its a semi permanent which fades with each wash and you wash your hair regulary because it does get greasy then yes it will make the colour fade quicker. If its a permanent/highlights it shouldnt make much difference. Have you tried a dry shampoo?
I'm not sure but I would assume so. Because the greece would loosen up the chemicals in the hairdye then your wash your hair and the loose chemicals wash out to.
I'm getting my hair coloured but my hair is greasy does this make a difference