Yes. Kronolith 2.0 introduced shared calendars. You can view as many calendars as you want in one overlaid view, and control access ot each of your calendars on a per-user basis.
Preliminary syncing support is available in the bleeding-edge development releases. See http://horde.org/sync/.
If your system administrator has configured it, and you have set an email address in your Horde preferences, you will get an email when an alarm "goes off".
Yes. Kronolith 2.0 supports the iCalendar/vCalendar format for importing and exporting and sending iCalendar invitations for e-mail based scheduling. As such it is now interoperable with any calendar/email system which can either send or receive standard iCalendar attachments. This means that you can create a kronolith event, send invitations for that event to any email addresses desired, and the email recipients can then add the event to their calendars automatically.