Oh… you’re using Contact. By design that removes the display of the email addresses. The assumption is that if Contact is installed that the email is not to be shown for security of the user’s email address … not making it public. If you want it public, there really is no need for Contact because the email address is “clickable”. When clicked it will open the users client email app and allow them to write the email from their app.
Both cMap and Market are pretty much the same template. The only functional difference is that once has a searchable category drop down (cMap) and the other has the categories listed to the side (Market). Any other difference are mostly cosmetic. Personally, I feel cMap is better design wise.
The custom field. That could be added, but they currently require a dev to add. Really it sound as if you really want a custom extension for Connections that can have the dues status tracked and send reminder emails. Using just a custom field and Contact is not going to achieve that.
Hope that addresses everything thoroughly!