刘海 is the famous immortal's name, he is mentioned here: https://en.wikipedia.org/wiki/Jin_Chan

刘海 is translated as 'fringe/bangs', 'the front part of sb's hair that is cut so that it hangs over their forehead'. The reason it is called '刘海' may come from a Taoist's name in ancient time.

1. Your translation is right. 2. it means bang on your forehead. Like, 她又瘦高又，刘海儿很长。 She is tall and thin, with her hair in long bangs,

Liuhair 刘海儿 is fringe/bang before your forehead. In Mandarin people pronounce this word with an -r sound at the end, though lots of southern people do not, in which dialects there is no -r sound therefore it's difficult for them to make the sound. The origin of this word is an old folk tale: a smart boy/young man called Liu Hai 刘海 fought and defeated the evil monkeys and their golden toad and form then on lived a peaceful and happy life(/ with his wife). There are some dramas in tradional Chinese operas, as 刘海砍樵 Liu Hai cuts firewood, 刘海戏金蟾 Liu Hai fools the Goden Toad.

刘海 means banged hair， named after a fairychild “刘海”.