Is this rude and manner less of my cousin 2 do so?

no not all american kids are like that some are and some are not like that i think he was going throw some changes tho but that is no excuses the way he treated you disrespectful you and you should stand your Ground with him and let him know that he can not treat you that way are disrespect you in anyway be strong don't just sit there and don't say anything let him know that your not going to take his rudeness anymore put your foot down and stand up for your self.