Re: Do these plugins exist…
1) s2member. You’ll likely need to download the zip and upload to your site via ftp ‘cuz it’s a huge plugin.
http://www.primothemes.com/post/product/s2member-membership-plugin-with-paypal/
2) Buddypress includes a private messaging system (kinda like internal email) but there are a few chat plugins available too. See this post:
https://buddypress.org/community/groups/miscellaneous/forum/topic/chat-rooms-chat-scripts-any-recommendations/
Hope this helps! 
