Can I book the meeting while chating with the bot?

For an interactive chat with a prospect, booking a meeting intently along with the chat will ge a good feature. The automated chat can ask the prospect whether you want to book the meeting with one of the expert. Then the bot can show the available open slots. Then prospect can select one of his/her interested slot and book the meeting. An email confirmation also can send at the same time. Do we have this feature with RASA?

Or can we integrate the RASA bot with the meeting booking apps like calendly?

I am very new to RASA and just exploring it. Please let me know if these features are already available.

A lot of what you are asking is doable and our demo bot already does some of it, you can talk to her on the docs page at Rasa Docs and the source code for how we do it is at GitHub - RasaHQ/rasa-demo: Sara - the Rasa Demo Bot: An example of a contextual AI assistant built with the open source Rasa Stack

You would have to build what you are looking for using the forms part of Rasa and a custom action server to take this information and make calls to a API or calendar system.