How to determine what image style an image field of a node has?
You can use the field_info_instance() function to get that information:

$entity_type = 'node';
$field_name = 'field_image';
$bundle = 'article'; // Or whatever content type you need.
$view_mode = 'default'; // Or whatever view mode you want to get settings for, e.g. teaser.

$info = field_info_instance($entity_type, $field_name, $bundle);

$settings = $info['display'][$view_mode]['settings'];

$image_style = $settings['image_style'];