Translation:My younger sister also wants iced tea.
You are correct. You will find that they actually use "little sister" as an alternative in a number of lessons later in the course. Same as "little brother" as a replacement for younger brother.
Consistency is not this course's strong point. Get ready to be marked wrong for many anomalies like this.
it's only said in like 15% of the US; you only see it in the rap community because it is usually used in african american communities or southern areas (mountain people, farmers etc.)
note- most mannerisms of the african american communities are considered 'cool' in america, as many white people try to act like black people to look strong and cool