Count occurrences of combinations of columns

Question 1

Function

While using the function addbusinessdays(), consider this instead:

CREATE OR REPLACE FUNCTION addbusinessdays(date, integer)
  RETURNS date AS
$func$ 
SELECT day
FROM  (
    SELECT i, $1 + i * sign($2)::int AS day
    FROM   generate_series(0, ((abs($2) * 7) / 5) + 3) i
    ) sub
WHERE  EXTRACT(ISODOW FROM day) < 6  -- truncate weekend
ORDER  BY i
OFFSET abs($2)
LIMIT  1
$func$  LANGUAGE sql IMMUTABLE;

Major points

Never quote the language name sql. It's an identifier, not a string.
Why was the function VOLATILE? Make it IMMUTABLE for better performance in repeated use and more options (like using it in a functional index).
(ABS($2) + 5)*2) is way too much padding. Replace with ((abs($2) * 7) / 5) + 3).
Multiple levels of CTEs were useless cruft.
ORDER BY in last CTE was useless, too.
As mentioned in my previous answer, extract(ISODOW FROM ...) is more convenient to truncate weekends.

Query

That said, I wouldn't use above function for this query at all. Build a complete grid of relevant days once instead of calculating the range of days for every single row.

Based on this assertion in a comment (should be in the question, really!):

two subsequent windows of the same firm can never overlap.

WITH range AS (              -- only with flag
   SELECT company
        , min(day) - 2 AS r_start
        , max(day) + 1 AS r_stop
   FROM   tbl t 
   WHERE  flag <> 0
   GROUP  BY 1
   )
, grid AS (
   SELECT company, day::date
   FROM   range r
         ,generate_series(r.r_start, r.r_stop, interval '1d') d(day)
   WHERE  extract('ISODOW' FROM d.day) < 6
   )
SELECT *, sum(flag) OVER(PARTITION BY company ORDER BY day
                         ROWS BETWEEN UNBOUNDED PRECEDING
                         AND 2 following) AS window_nr
FROM  (
   SELECT t.*, max(t.flag) OVER(PARTITION BY g.company ORDER BY g.day
                           ROWS BETWEEN 1 preceding
                           AND 2 following) in_window
   FROM   grid     g
   LEFT   JOIN tbl t USING (company, day)
   ) sub
WHERE  in_window > 0      -- only rows in [-2,1] window
AND    day IS NOT NULL    -- exclude missing days in [-2,1] window
ORDER  BY company, day;

How?

Build a grid of all business days: CTE grid.
To keep the grid to its smallest possible size, extract minimum and maximum (plus buffer) day per company: CTE range.
LEFT JOIN actual rows to it. Now the frames for ensuing window functions works with static numbers.
To get distinct numbers per flag and company (window_nr), just count flags from the start of the grid (taking buffers into account).
Only keep days inside your [-2,1] windows (in_window > 0).
Only keep days with actual rows in the table.

Voilá.

SQL Fiddle.

Question 2

Basically the strategy is to first enumarate the flag days and then join others with them:

WITH windows AS(
SELECT t1.day
       ,t1.company
       ,rank() OVER (PARTITION BY company ORDER BY day) as rank
FROM table1 t1
WHERE flag =1)

SELECT t1.day
      ,t1.company
      ,t1.flag
      ,w.rank
FROM table1 AS t1
JOIN windows AS w
ON
  t1.company = w.company
  AND
  w.day BETWEEN 
 t1.day - interval '2 day' AND t1.day + interval '1 day'
ORDER BY t1.day, t1.company;

Fiddle.

However there is a problem with work days as those can mean whatever (do holidays count?).