And can Group events be separate from over all events, so a member sees both general events and just their group events in the calendar, and non members only see events relevant to them? 

I suggest you can make all groups private so that only members can view the content.

>>if it is possible to configure this so people see their group content in addition to overall site content easily, but not see content from groups they aren't members of? 

Have you had a chance to see how "Dashboard" page works?

Dashboard is the page where user sees content related only to him.

Newsfeed within the dashboard shows activities that are user related only.

So may be renaming "Dashboard" to something more personal will work? For example renaming  it to " My Timeline"/"My Home" will give a user a hint that what he sees there is personal and he won't get any unrelated items there. 

If one day user wakes up and decides that he would like to know what is going on in the world, he can just visit your main page and see sitewide activities there.

>>In the events area, is there a way to have event details transfer to user calendars? We have a Google Calendar set up now, but was thinking a more integrated calendar would be more powerful.

Requires custom code modifications.

>>Is there a way to add users and their group assignments enmasse, or is the only way to have them invited, and then configure their memberships themselves? 

1. Manually via database. Let me know if you are interested in digging into this and I will provide more detailed instructions. 

2. You can get a plugin that makes admin friends with all site users. This should make your life easier when you decide to invite users. Otherwise you will have to manually add each user as a friend. Search the Store by "friends" keyword, and you should find this plugin. Note, as far as I remember it is a third party plugin, so if you get any questions about it, you will need to contact plugin developer.

The bigger help was seeing the configuration button for the groups plugin and turning on forums (or was it in the forums plugin, I can't remember now). Bummer that some of the other features I needed had to be bought. Group specific documents, photos, videos. Now we just need a group events plugin.