Google Calendar – How to Show a List of Events

Currently on a web site that I help administer, we have a custom built calendar built with PHP. The web site is for a performance group, and they have various categories of performances. For simplicity, lets say they have two, dancing shows and singing shows.

We're considering switching to Google Calendar, in order to be able to share the calendar with other sites and other collaborative features that the service offers.

However, we don't want to lose the functionality we have now, mainly to do with how the calendar displays on the group's web site. There are three conditions which call for different calendar views.

1. One condition is the group's overall schedule, which is a standard
   view by calendar month. This is the default Google Calendar display
   option, so no problem there.
2. The other condition is to display the next 3 upcoming events by
   category. So on the dance events page, we want to see a list of the
   next three dance events. If I have the terminology right, this is an
   "agenda" view, but I'm not sure about that. So on this page the
   embedded calendar object would need to filter for just dance events.
   Similarly, on the singing page, the embedded calendar would need to
   filter for singing events.
3. The last condition is to show upcoming events of all types. So this
   would show the next 3 events of dance and singing together, in a
   list, ordered by date.

I am unclear on whether or not events can be categorized by type for filtering purposes, and if calendars can be displayed in a list style. I've seen mention of an "agenda" view, but I haven't been able to discern exactly how one enables it.

Are these requirements possible, and if so, how?