OK, yes, I confused that, meaning the display of a group and according blogs page with the joined group page.
My issue with the latter is that I can't find how to make that work from the menu.
GJ doesn't have blogs so I suppose you'd just use a module to display the blogs on the GJ page by assigning it to GJs menu item, which you can generate from GJs backend.
The second problem is the largeness of the group name, icon and details. It is so large that you have to scroll down to see the blogs.
You can restyle using CSS or edit the entire GJ frontend. Please see the below location for GJs template files.
Maybe you have a tutorial on that (GJ customization)? So far I wasn't able to find it.
Nope, they're just PHP files with mostly HTML in them. You can find template files at the below location and edit them as needed or copy them to your own template folder, edit, and select from backend (preferred method).
components/com_comprofiler/plugin/user/plug_cbgroupjive/templates/