How to import data from another website using an API link?

First, that echo '<script src="https://www.gmodules... seems completely unrelated to the question, isn’t it?

Second, that API is for a paid service without a public API, so we cannot answer for their “api answer”. Ask their support.

What you are looking for is wp_remote_get. Normally, the response from an API is a Json string. But in the case of this service, the Json seems mal-formed. At least, it is not being decoded by json_decode.

So, as far as WordPress is involved, this is what you need to get that data. How you’re going to deal with it is off-topic here, try at StackOverflow.

if( !class_exists( 'DevMind_DashboardWidget') ) 
{
    class DevMind_DashboardWidget 
    {
        function devmind_dashboard_widget() 
        {
            $content="http://serpbook.com/serp/api/?viewkey=dw8628r&auth=678a498d500a203885191bdd16c70190";

            $api = wp_remote_get( 
                $content, 
                array( 
                    'timeout' => 120, 
                    'httpversion' => '1.1' 
                ) 
            );

            if ( $api['response']['code'] == '200' )
            {
                // This does not work
                $api_array = json_decode( $api['body'] );   
                echo '<pre>DECODED:<br>' . print_r( $api_array, true ) . '</pre>';

                echo '<pre>ORIGINAL:<br>' . print_r( $api['body'], true ) . '</pre>';
            }
        }

        function devmind_add_dashboard_widget() 
        {
            wp_add_dashboard_widget( 
                'devmind-custom-widget', 
                'Campaign Manager', 
                array( 'DevMind_DashboardWidget', 'devmind_dashboard_widget' ) 
            );
        }       
    }

    add_action( 
        'wp_dashboard_setup', 
        array( 'DevMind_DashboardWidget', 'devmind_add_dashboard_widget' ) 
    );
}