"May" is the correct word for all of your examples. Informally, one can use "can", but it isn't correct grammar. "Can" in this context means you are asking if you are able to know something.
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Wonder123May I know why you are requesting to replace the color.May I know why you are requesting to replace the color.May I know the reason for your requestCan I know the reason for your requestMay I know the reason for itCan I know the reason for itMay I know why you are making this request.Can I know why you are making this request.All of those need questi