Not the cleanest query ever... but is this what you are looking for?
SET @year := 2013;
SELECT
CASE WHEN CONCAT(@year, '-01-01') BETWEEN date_ini AND date_end THEN CONCAT('id', id) END Jan,
CASE WHEN CONCAT(@year, '-02-01') BETWEEN date_ini AND date_end THEN CONCAT('id', id) END Feb,
CASE WHEN CONCAT(@year, '-03-01') BETWEEN date_ini AND date_end THEN CONCAT('id', id) END Mar,
CASE WHEN CONCAT(@year, '-04-01') BETWEEN date_ini AND date_end THEN CONCAT('id', id) END Apr,
CASE WHEN CONCAT(@year, '-05-01') BETWEEN date_ini AND date_end THEN CONCAT('id', id) END May,
CASE WHEN CONCAT(@year, '-06-01') BETWEEN date_ini AND date_end THEN CONCAT('id', id) END Jun,
CASE WHEN CONCAT(@year, '-07-01') BETWEEN date_ini AND date_end THEN CONCAT('id', id) END Jul,
CASE WHEN CONCAT(@year, '-08-01') BETWEEN date_ini AND date_end THEN CONCAT('id', id) END Aug,
CASE WHEN CONCAT(@year, '-09-01') BETWEEN date_ini AND date_end THEN CONCAT('id', id) END Sep,
CASE WHEN CONCAT(@year, '-10-01') BETWEEN date_ini AND date_end THEN CONCAT('id', id) END Oct,
CASE WHEN CONCAT(@year, '-11-01') BETWEEN date_ini AND date_end THEN CONCAT('id', id) END Nov,
CASE WHEN CONCAT(@year, '-12-01') BETWEEN date_ini AND date_end THEN CONCAT('id', id) END `Dec`
FROM
policies
WHERE
date_end >= CONCAT(@year, '-01-01')
AND
date_ini <= CONCAT(@year, '-12-01')
But I think that it's usually better to represent the results using some code, eg. with PHP, rather than using a MySQL query.
Fiddle is here.
Edit
And this query is for the sum:
SET @year := 2013;
SELECT
SUM(CONCAT(@year, '-01-01') BETWEEN date_ini AND date_end) Jan,
SUM(CONCAT(@year, '-02-01') BETWEEN date_ini AND date_end) Feb,
SUM(CONCAT(@year, '-03-01') BETWEEN date_ini AND date_end) Mar,
SUM(CONCAT(@year, '-04-01') BETWEEN date_ini AND date_end) Apr,
SUM(CONCAT(@year, '-05-01') BETWEEN date_ini AND date_end) May,
SUM(CONCAT(@year, '-06-01') BETWEEN date_ini AND date_end) Jun,
SUM(CONCAT(@year, '-07-01') BETWEEN date_ini AND date_end) Jul,
SUM(CONCAT(@year, '-08-01') BETWEEN date_ini AND date_end) Aug,
SUM(CONCAT(@year, '-09-01') BETWEEN date_ini AND date_end) Sep,
SUM(CONCAT(@year, '-10-01') BETWEEN date_ini AND date_end) Oct,
SUM(CONCAT(@year, '-11-01') BETWEEN date_ini AND date_end) Nov,
SUM(CONCAT(@year, '-12-01') BETWEEN date_ini AND date_end) `Dec`
FROM
policies
WHERE
date_end >= CONCAT(@year, '-01-01')
AND
date_ini <= CONCAT(@year, '-12-01')
Fiddle here.