How to get all posts belongs to a user between a certain date

Check out the WP_Query reference.

For parameters.

Date Parameters.

$args = array(
    'author' => 123 ,
    'date_query' => array(
        array(
            'after'     => 'January 1st, 2013',
            'before'    => array(
                'year'  => 2013,
                'month' => 2,
                'day'   => 28,
            ),
            'inclusive' => true,
        ),
    ),
    'posts_per_page' => -1,
);
$query = new WP_Query( $args );

For the word count check out this post. It has a quick way of doing it by using explode get the post content and then using explode and count.