Translation:My classmate is tall.
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.
No. It would have to be "classmate's", but we don't really describe a height as tall, only a person or a thing, so we don't say "My classmate's height is tall".
"My classmate's height is six foot two" is possible, though I'd probably just say "My classmate is six foot two".