There are some good English teachers that have had to learn English as a second language before they could teach it. However, there are several reasons why many of the best schools prefer to hire native English speakers. One of the reasons is that native speakers have a natural flow to their speech that students of English should try to imitate. The closer ESL / EFL students can get to this rhythm or flow, the more convincing and comfortable they will become.
This is not only a fun way to learn but it is also very effective. By watching English films (especially those with English subtitles) you can expand your vocabulary and hear the flow of speech from the actors. If you listen to the news you can also hear different accents.
Music can be a very effective method of learning English. In fact, it is often used as a way of improving comprehension. The best way to learn though, is to get the lyrics (words) to the songs you are listening to and try to read them as the artist sings. There are several good internet sites where one can find the words for most songs. This way you can practice your listening and reading at the same time. And if you like to sing, fine.
Only by studying things like grammar and vocabulary and doing exercises, can you really improve your knowledge of any language.