Translation:My classmate is tall.
I don't think there's any additional information conveyed, but the translation could be rendered as "my classmate is tall in stature".
This sentence has a Topic-Comment structure.
Subject (我的同学) + Topic (个子) + Comment (很高)
我的同学很高 is a perfectly acceptable sentence. However, many (perhaps most?) native speakers with add 个子 as a Topic. Often the Topic seems to limit/clarify the scope of the comment in sentences that are open to multiple interpretations. (For example, 她年纪很大, lit. "She is great in age.") My sense is 我的同学很高 completely unambiguous. I think 个子 is added merely for rhythm.
Perhaps. I wouldn't use 个子, and no one I know would either. However, there is nothing wrong with putting it in.
On another note, this sentence usually refers to one classmate.