Unless I'm misstaken, the life cycle of version 4.1 ended more than 2 years ago, which means you should most definitely upgrade to 5.5.
In this thread I explain why, when a group by clause is present, every selected field must be part of the group by clause or be part of an aggregate function. This is always the first thing to fix before doing anything else. So, if you really need to select c.*, then you also have to put every single field from c in the group by clause.
Once done with that, you should also ditch one of the two joins on rr_references. Consider two tables, a and b. Table a contains one row which is joined against 4 rows in b.
SELECT a.id, b.id
FROM a
LEFT JOIN b ON a.id = b.a_id
Thus, the above will select 4 rows. How many rows will be selected if you join on b again?
SELECT a.id, b.id
FROM a
LEFT JOIN b ON a.id = b.a_id
LEFT JOIN b AS b_again ON a.id = b_again.a_id
Well, since you now have 4 rows containing a.id (one for each matching row in b) and you know that each such row will match 4 rows in b_again, the answer is 4*4 = 16 rows.
And finally, you can count both taken surveys and those not yet started / completed in one go with one single join on that table. Once again, a little example. Two tables, aa(id, title) and ab(id, a_id, txt), a_id REFERENCES a(id).
aa contains (1, 'music') and ab contains (1, 1, 'Ben Klock'), (2, 1, 'Len Faki'), (3, 1, 'Dinky') and (4, 1, null).
SELECT a.title, COUNT(*)
FROM aa a
LEFT JOIN ab b ON a.id = b.a_id
GROUP BY title
will obviously give you a count of 4 for music. However, you can always group on null / not null or string length 0 / greater than 0 etc.
SELECT a.title, ISNULL(b.txt) AS bnull, COUNT(*)
FROM aa a
LEFT JOIN ab b ON a.id = b.a_id
GROUP BY title, bnull
Since you are now grouping on title (music) and bnull (null or not null), you will get your results split up into a count of 3 (music and not null) and 1 (music and nul). The same thing can be done with string length if that's needed
SELECT a.title, COUNT(*), CHAR_LENGTH(txt) = 0 AS zerolen
FROM aa a
LEFT JOIN ab b ON a.id = b.a_id
GROUP BY title, zerolen