Taiwanese band, Sunset Rollercoaster, covered an old Chinese pop song "我是一隻魚", which meant "I'm A Fish" in English, sung by 任賢齊. Taiwanese band Sunset Rollercoaster covered an old Chinese pop song "我是一隻魚", which meant "I'm A Fish" in English, sung by 任賢齊.

The commas should be deleted because the name of the band is essential information (if you were to omit it, the sentence would no longer make sense and would be grammatically incorrect).

The Taiwanese band, Sunset Rollercoaster, covered an old Chinese pop song "我是一隻魚", which meants "I'm Aa Fish" in English,. It was sung by 任賢齊. The Taiwanese band Sunset Rollercoaster covered an old Chinese pop song "我是一隻魚" which means "I'm a Fish" in English. It was sung by 任賢齊.

The Taiwanese band, Sunset Rollercoaster, covered an old Chinese pop song "我是一隻魚", which meant s"I'm A Fish" in English,. The original was sung by 任賢齊. The Taiwanese band, Sunset Rollercoaster, covered an old Chinese pop song "我是一隻魚", which means"I'm A Fish" in English. The original was sung by 任賢齊.

Unlike in Chinese, in English you must connect clauses with conjunctions or otherwise break them up into multiple sentences.

They re-edited the song with their(or: in) their (own) authentic style. They re-edited the song with (or: in) their (own) authentic style.

“In their own” sounds more natural, but the original sentence is also grammatically correct.

They re-edited the song within their own authentic style. They re-edited the song in their own authentic style.

They re-ediinterpreted the song with their own authentic style. They interpreted the song with their own authentic style.

A good word to use would be "interpret" -- putting their own spin on it-- since you said the new song is influenced by their own style. It is good to indicate that the style is authentic to THEM by saying "their own authentic style"

The song was a nod to the 90's golden era of Chinese pop (song golden eras). The song was a nod to the 90s golden era of Chinese pop (songs).

“Songs” isn’t necessary. I assume you are saying that the 90s were the golden era of Chinese pop.

The song was a nod to the Golden Era of 90's Chinese pop song golden eras. The song was a nod to the Golden Era of 90's Chinese pop songs.

The song was a nod to the 90's Golden Era of Chinese pop song golden eras. The song was a nod to the 90's Golden Era of Chinese pop songs.