Yes that addresses the first issue. 

If I understand you correctly on the second issue it would work something like this:

In a logical place in Studio:

Allow group Admins to select content:  Yes/No

Default Group Content (independent of above)

[  } Discussions            

[  } Events

[  } Albums

[  } Polls

[  } Videos

[  } Files

[  } Recipes

Then, on the create/edit group page, allow the addition of content that Isn't checked off in Studio as default group content.  This way, site admins could also restrict certain content form groups. by selecting default content, and disallowing Group admins the ability to change things. (In case people start creating private groups to use as a file repository)