WordPress doesn't seem to support multiple blogs without multiple installation
It does. It's called Multisite. It's even got its own forum here. :-)
See create a network.
To the right of the page there are dynamic features which should display the most recent "news", "blog entries", and "calendar events".
You'd need to define what you mean by "recent news" in the context of a multisite set up. Extracts from the various sub-sites can be displayed in the top level site using various approaches. With regard to events, you'd need to decide whether you want to stay with the Google Calendar or move to an event management plugin (of which there are many).
HTH