I would like about 4 groups (set up by super admin) available for members to choose from. Can I do something like this?

Yes, first create a category for your groups within GJ > Categories. Next create your 4 groups in that category within GJ > Groups. Next navigate to GJ > Menu and generate a menu item to the overview page or your Category page. Now you users can navigate to that menu item and join groups as needed.

Is there an article or video on setting up and using Group Jive?

There's some videos that you can find on the GJ page below.

www.joomlapolis.com/cb-solutions/groupjive

There's also a quick configuration tutorial that you can find below.

www.joomlapolis.com/support/tutorials/111-picture-books/18268-community-builder-groupjive-quick-start

I want to create good communication - something like facebook for just the members (not the public) Maybe have one main group "All Choir Members" and 4 sub groups (soprano, alto, tenor, base)

GJ Categories and Groups can have access permissions. So some could be public, others for registered users, etc..

Can I set something up so everyone would get an email if a new blog entry is made?

It's possible, but you'd have to develop a plugin to do this or loop every user and email them using a Code action and PHP. I however suggest you do not do this as your domain will quickly be marked as a spammer by email providers. It's better to use a newsletter system with scheduled newsletters or something of the sort that's less prone to abuse.

Do I need the “connections” system?

I've no idea. That depends entirely on what you intend to do with your site. Without it users can't establish connections with one another (e.g. Friends like on other social sites).

Does private messaging do the same thing?

No, they're two entirely different things. PMS allows users to send private messages to one another and nothing else.

I am thinking I will not need the “profilebook” since I have groupjive – that is a better “wall” program?

It's another situation of two entirely different things. The GJ Wall integration is for adding a Wall to Groups. The CB ProfileBook Wall will add a Wall to the users profile.

Do I really need the “myinvites” system? I do not want to make members need an invitation to join a group. Can I get rid of it? Not use it?

GJ Invites feature? No, you don't have to use it. You can shut it off within GJ > Config > Groups > Invites by setting "Display" to "Disable". However you won't be able to use invite only groups by doing this a you won't be able to invite anyone.

There is a “My Categories” on the menu. I only have one category – can I get rid of the menu link?

Menu? You mean the profile tab? Yes, within GJ > Config > Tabs > Categories set "Display" to "Disable".

I still do not understand what good the blog is if no one knows you have made a post?

Sending emails is not the solution for this. It just becomes spam and people learn to avoid your site because of it. CB Activity normally would be the solution here as users could see who created a blog, but it's not yet compatible with CB 2.x so it can't track CB Blogs right now.

CB Blogs however integrates directly into the CMS. So if you've set the model to Joomla or K2 you can use normal Joomla and K2 content display features to showcase or inform users of blog posts. For example you could have a module that shows most recent Joomla content entries or even your front page could show the blog category posts.

If you post on a group, does anyone get notified of the post? I need a way to make a post somewhere where everyone will get it.

For GroupJive, yes. The user needs to click Notifications on the GJ menu when viewing the group. They can then subscribe to new wall posts. You can also enable this by default within GJ > Configuration > Integrations > Wall > Notifications > Defaults, but I recommend setting GJs notifications to PMS instead of Emails or you risk the same issue of being labelled a spammer by email providers depending on how active your site is.

Can users be automatically be connected to someone or automatically subscribed to a group?

Yes to both. You can establish a connection automatically with a specific user using CB AutoWelcome. You can also use CB Auto Actions and its Connections action.

For groups you can use the GJ Auto Integration included with GJ and let them select a group at registration using the auto fieldtype. You can also use CB Auto Actions and its CB GroupJive action to force them into groups.

Could there be a master user that eveyone is "connected?" to that can send out a post to everyone.

You can auto connect everyone to a specific user using CB AutoWelcome or CB Auto Actions and the Connections action. I've no idea how you intend to mass post to everyone though.

2 more questions - when I go to Private Messaging and select compose - there is nothing in the userlist - how do I get the list to show.

You need to be connected to users. That dropdown shows your connections. Alternative is configure UddeIM to show every user instead of just connections.

Is there a way to add a joomla menu to the tab system?

A Joomla menu as a tab? Don't understand, a tab is do display content; it's not a menu system. If you mean CB Menu as a new menu item then yes using CB Auto Actions.