Please see my answer in https://forum.mendix.com/questions/3864/Generating-CODE. In short, yes you will need the server as there is no generated code.
The Mendix Rich Webclient is simply the client ran in the browser that talks to the server. I'm not sure where the term connectivity manager is used but I think it is referring to the database connectivity part of the server. Where did you find this term?
Edit: Yes in those slides the connectivity manager refers to the database connectivity part of the server.
I suggest playing around with Mendix for a while and seeing how it works.