1. First of all, is it possible to build a Chatbot agent using Copilot Studio, for a public facing website?
--Yes it is, but you have to turn off Authentication, well.. ok thats not completely true, but you said Public Facing which to me means Anonymous so yes, turn off authentication to publish it there,. In the Publish Tab of your Agent, is a Demo Public site you can publish too for demonstration and testing purposes
2. If so, Is it possible to embed this agent into their public website? If so how?
--You generate an embed code, and use that to embed and publish. Like with other embeddable things, its the same
3. how does the agent distinguish between an internal person using the chatbot, versus a external user asking questions in the chatbot?
--It does not. If you have an anonymous agent, it does not get your email address or user names or anything, its all anonymous. Technically you could use IP addresses as a way, if the customer has a specific set of IP ranges, but by default there is no way for it to no because.,. well,.. its anonymous
If these suggestions help resolve your issue, Please consider Marking the answer as such and also maybe a like.
Thank you!
Sincerely, Michael Gernaey