When I click on the Download Event as shown below a calenderevent.ics file is created.

When I import the .ics file it creates an event in your email client as shown below:

If a member clicks on "Accept", Tentative" or "Decline: one would assume that the response would be sent to the appropriate calander and processed.  I don't believe that is the case, but I may be wrong.

Does the calendar app indeed accept responses or not?  If it does how do I setup my site to accept those responses?

If it doesn't, why are you including the "Respond" options in the imported .ics file?

 

This would not be a functional part of the calendar application. The respond feature there is from an event in the calendar client you're using (in this case Outlook), I'm afraid, it is not connected to the RSVP feature in our software.