Yes. Bot integrations have been launched on multiple pages to provide a different experience on each page.
While the usual conversion rates for the Leads through Website/Lead ads/Google adwords hovers around 4-5%, a Messenger-engaged user converted at a double rate (9-11%).
Though through the UI dynamic answers cannot be done except for AI based questions, we can alter the flow if the use-case is worthy of it to include dynamic replies
For text based Q&A, Watson AI is used to provide intelligent responses. The general structure of the bot is flow based IFTTT type of a model.
Yes, you can broadcast a message to all those who have messaged the page at least once.