Re: Custom Group Pages
I don’t know of any existing efforts to customize group images or backgrounds, but it does sounds like a good idea for a plugin. Using the group exension API (https://codex.buddypress.org/developer-docs/group-extension-api/) it’s fairly easy to add another page to the group admin menu. You could call this menu “Display options” and let group mods change settings. You’re plugin could then check the settings, and display stylesheets/banners as appropriate. It would take some development time, but I think it could work smoothly.
This would of course be heavily theme-dependent, not only for the implementation (div position and such) but also for the design (changing the backgrounds while keeping the feel of the theme).