How do i create a loop that list and divide posts into months?

you could do this in any loop by checking the current post’s published month, and printing it when it changes:

<?php
// set current month to that of first post, and print it.
$current_month = get_the_time('F');
echo $current_month;

while (have_posts()) : the_post();

    // check each subsequent post to see if the month is the same
    // or has changed and needs to be printed:
    $this_month = get_the_time('F');
    if( $this_month!=$current_month ):
        $current_month = $this_month;
        echo $current_month;
    endif;

    // output data for the post
    the_title();

endwhile;

?>