Does Firefox have Email

I don't think so at the moment. There is a project in development called Thundermail. See: What is Thundermail. If it sounds intriguing, you can join the wait list.

If you are looking for a new email service right now, there obviously are the free ad-supported ones like Microsoft and Yahoo. There are some more privacy-oriented ones with a good reputation such as Protonmail.

Does Firefox offer their own email like Google offers Gmail?

Firefox is a web browser and not a company or such. Mozilla the makers of the Firefox web browsers does not have a email service for the general public. They do manually provide @mozilla.org @mozilla,com email addresses to those who work for Mozilla in a capacity that warrants getting one and have to give it up when they leave.

Thunderbird is developed and operated by MZLA Technologies Corporation, a wholly owned subsidiary of the Mozilla Foundation. They do have their own email service that you have to sign up and pay for to use as mentioned which is Thundermail.