How widespread is the use of 妳? When addressing a female, do I have to use 妳 instead of 你?  

How common is the usage of 妳?
Mainland China doesn't use 妳 anymore. 妳 is mostly used in Hong Kong and Taiwan where they still use Traditional Chinese.

As you mentioned in the question, 妳 is used to address a female person. In mainland China, people use 你 for both males and females.

Note: the right hand side of 你 or 妳 is 尔. In Traditional Chinese, 尔 is written as 爾. However, as far as I know, 你 and 妳 in Traditional Chinese are not written as 儞 not 嬭 but just 你 and 妳.