To edit the group, you can either:
double click on any geometry in the group.
open ... more tools (in the drawing toolbar) -> groups -> edit group
This enters group edit mode.
The feature tools are shown in dark blue in group edit mode.
Edit individual geometries within the group.
Click off the group to end group edit mode.
To add more items to the group, either ungroup the existing group and create a new one, or select the geometry you want to add and the group and then create the group again