Hi Stephen

Have discovered your post - 

Q1: What are the opportunities for branding/theming at the 'Group' level, other than uploading an image to the top of the Group?

There isn't an ability to allocate a theme to a group unfortunately in Social but it is possible to allow users to choose a theme when creating a page. 

(Configure Site > Site options > User settings) this would require the theme to be created. 

In Mahara which Social is based on there are skins which are user friendly ways to change appearance of pages see http://manual.mahara.org/en/16.04/portfolio/skins.html - skins aren't  implemented in Social - not sure of the plans for this there may be issues I am not aware of.

Q2 

I tested this out when an idea is proposed and you select share to everyone people in other tenants can view your idea irrespective of groups. Groups can be created across tenants - you can invite others or make open groups or request membership. 

I don't think when you belong to more than one tenant you choose which institution you have logged in from  there is only  have one authentication method (login) per user so would login from the same tenant. You would be able access content from both tenants though.

Hopefully that clarifies things