have an operation on sb

不行
要用 have sb operated
have an operation on 是接受手术
补充一下
operate on sb是对的 代表对某人动手术
do an operation/perform an operation +on sb's+身体的某部位 也是对的
但是对某人动手术不用 have an operation on sb
某人接受手术要说
sb have an operation on sb's +身体的某部位
或 sb have an operation for 疾病名称 -----某人为了某种病动手术

都可以啊，呵呵O(∩_∩)O~
例如：外科医生为她做阑尾切除手术。可以翻译为
The surgeon operated on her for appendicitis.
或者 The surgeon had an operation on her for appendicitis.

是的