When someone uploading an images how can we manage that they are not to big, it is possible to downsize those to lets say 500×500 automatically?

>> There is no automated solution for this. However using the below code you can add restriction on this :

function resize_resolution($file) {
$image = getimagesize($file['tmp_name']);
    $minimum = array(
        'width' => '400',   //set your minimum
        'height' => '400'
    );
    $maximum = array(
        'width' => '2000',  //set your maximum
        'height' => '2000'
    );
    $image_width = $image[0];
    $image_height = $image[1];

    $too_small = "Image dimensions are too small.";
    $too_large = "Image dimensions are too large.";

    if ( $image_width < $minimum['width'] || $image_height < $minimum['height'] ) {
        $file['error'] = $too_small; 
        return $file;
    }
    elseif ( $image_width > $maximum['width'] || $image_height > $maximum['height'] ) {
        $file['error'] = $too_large; 
        return $file;
    }
    else
        return $file;
}
add_filter('wp_handle_upload_prefilter', 'resize_resolution');