Unknown column 'actions_in_group' in 'field list'
The SUM should be on actions_in_user_group, not actions_in_group

Same goes with actions_in_user_collection

I also added groupby_stream_date to assist with the group by 

SELECT *, 
   SUM(actions_in_user_group) AS total_rows_in_group,
   GROUP_CONCAT(actions_in_user_collection) AS complete_collection
   FROM (SELECT stream.*,date(stream.stream_date) groupby_stream_date,
          COUNT(stream.id) AS actions_in_user_group,
          GROUP_CONCAT(stream.id) AS actions_in_user_collection
       FROM stream
       INNER JOIN follows
       ON stream.user_id = follows.following_user
       WHERE follows.user_id = '0'
       GROUP BY stream.user_id,
            date(stream.stream_date)
     ) As something 
   GROUP BY object_id,
            groupby_stream_date
   ORDER BY groupby_stream_date DESC;