I'm not too sure this is very useful. I think it is much better to track your visitor with Google Analytics or PiWik (which is what we usually do), but it should be rather easy to accomplish:
that's it.
That would have to be programmed if you want a specific button, but you can try this:
Yes, this can be done. To activate this behavior two steps need to be taken. First, each user that wants this needs to go to their preferences screen and uncheck the “Internal Email Client” option. This option, which is checked by default, will open the application send email screen. When unselected the default browser behavior takes over. By default the browser will open the email client configured in the operating system but that can be changed in each browser. So our second step is to configure the browser to open GMail as can be read here:
I was able to make it work in Windows/Chrome, with the following conditions: