Once you open a web map, you'll see an Add button at the top that allows you to add more layers to the map.
You can configure the gallery from the My Organization page to point to one of your groups. If you want people in your organization to be able to see the items, they must be shared with the organization. It would be possible to let different people in your organization see different items by sharing them with the gallery group and with specific groups users are members of.
Thanks,
Mike