Hi, @monsur
WP-Chatbot has PRO feature which is Answering Service where you can specify few questions to gather lead information like email, phone number, company name etc. and send it to your email once someone interacting with it.
Chat widget could be installed on any website, it is linked to the bot.
Talking about the email list, do you mean like gather lead data and send it to mailchimp? If so, yes it is possible in the web version of MobileMonkey app https://app.mobilemonkey.com/
We provide Zapier integration between MobileMonkey and MailChimp, so once your bot catches the data it is sending to MailChimp and later you can proceed with an email campaign for those contacts.
Let me know if you have any questions