英语翻译请问句中的likes是否正确?即句中likes这个第三人称形式是否用对了,顺便讲下原因.

LZ,相信你自己,翻译无误.
I don't think her mother likes her new look.是个宾语从句,主句为I don't think,宾语从句为Her mother likes her new look.（要注意,宾语从句独立出来的意思要理解成“不喜欢”）,主句、从句之间省略了that,还原为完整句式为I don't think that her mother likes her new look.从句动词时态不受主句影响.
又,其实“形象”用得更多的是image、appearance或figure,look较少用.