Can we get user details like mail etc through api in publish environment.
There is no out of box functionality to expose user details via rest API's, you need to write custom logic.
Things you need to consider:
You are trying to expose user details, as it is PII data, so you need to consider security, you must enable authentication.
If security is not a concern then you can also create servlets and expose user details in JSON format.
You can use watch below link to get some idea on exposing aem content via rest ap's
You can integrate AEM with Spring and expose data.