1. Do you want people to register for events of just provide the information about registration details - if you want to give the information
e.g. registration times, capacities, contact telephone numbers etc. then the custom fields addon will probably help (Silver member addon). If you want people to register then you would want RSVP Pro (Gold member) - see the demo videos here
http://www.jevents.net/jevents-club/demo-videos
2. This is standard JEvents functionality - you setup the permissions in the JEvents config (permissions tab)
3. This is standard JEvents functionality - create an iCal export menu item.
4. You want to auto-create entries in Facebook/Twitter? if so then you would want the Silver member addons and maybe link in to AutoTweet NG (a non-Jevents addon for Joomla). We also offer a Facebook share/like/comments silver member addon
5. What other sort of communication/interaction are you looking for? Its possible that JomSocial or Community Builder would be good for you but they may also be overkill