Hi, Ali. Thanks for your interest in our plugin suite.
You can view a demo of our ticketing plugin at our demo site: http://wpshindig.com/event/events-tickets-demo/
Tickets are handled fully on the site, not via email.
Our single event pages (on which they obtain the ticket/RSVP), do allow importing to their own calendar app.
There is an Attendees Report per event.
All this is possible with just the free versions of The Events Calendar and Event Tickets.
Event Tickets Plus enables you to sell tickets, not just do free/RSVP tickets. Plus, it allows you to ask for Attendee Information per purchased/reserved ticket.
Last but not least, we have a pretty great Refund Policy so you can buy one or many of our add-ons and thoroughly test them.
I hope this info helps. Let me know if you have any follow-up questions.