When you have a query that isn't returning enough results a good way to diagnose it is to remove constraints on the query until you get some rows back.
So...

;WITH myTable as
(
SELECT *
  FROM (VALUES (1001, 'X'),
               (1002, 'YY'),
             ...

If you set your variable to a csv string e.g.:
DECLARE @Subjects as nvarchar(100) = 'economics,maths'
Then use a string splitter function to convert search value into a...

The things I'd try are:
1. Change the stored procedure to stop parameter sniffing.
2. Make sure your statistics are up to date.
3. Drop the current index on dbo.SUBMISSION_QUESTION_ANSWERS(DOCUMENTID,REVISION) and...

How many rows does this table have?
A good index for this query would be:
CREATE INDEX IX_SUBMISSION_QUESTION_ANSWERS_1
ON dbo.SUBMISSION_QUESTION_ANSWERS(DOCUMENTID,REVISION,CONTEXT,RANK,SUBMISSION_QUESTION_DEFINITION_ID)
Why are you using WITH (NOLOCK)?

select f.*,
   IIF(T.LEFT_OVR_ONHAND<0,0,T.LEFT_OVR_ONHAND) LEFT_OVR_ONHAND,
   IIF(T.LEFT_OVR_ONHAND>0,0,-T.LEFT_OVR_ONHAND) RequiredQuantityTotal
from #f f
cross apply(values (f.OnHand-f.RequiredQuantity)) T(LEFT_OVR_ONHAND)

You could try these indexes, then look at the execution plan to see which ones are used and drop them if the aren't:
CREATE INDEX IX_T_PROD_TEXT_F_PRODUCT ON T_PROD_TEXT(F_PRODUCT,F_DATA_CODE);