Brendan was not only a great dancer and he was a great choreographer.

Correct sentence- Brendan was not only a great dancer, but he was also a great choreographer.

Saying that something is not only a dancer but a choreographer means that he is a dancer as well as a choreographer.

Throughout this year, the music of David was far more popular among audiences in Australia than John Peterson.

Correct sentence- Throughout this year, David’s music was far more popular among audiences in Australia than John Peterson’s music.

In the above sentence, music (thing) is being compared to John Peterson (person). In order to make the sentence correct, we must compare music to music.

According to research, the findings established that chimpanzees often possess skills similar to humans.

Correct sentence- According to research, the findings established that chimpanzees often possess skills similar to the skills of humans.

The first sentence is incorrect as it implies that the skills themselves are similar to humans, which is not the intended meaning. The second sentence is correct as it specifies that the skills possessed by chimpanzees are similar to those of humans.