1. Is can any shortcode be wrapped in a php tag like <?php [aec_events organizer=100], ?> or something like that?
Try using,
<?php echo do_shortcode('[aec_events organizer=100]'); ?>
2. How can I dynamically get the event or organizer ID?
I would need some more details like where and why you need to get these IDs. Also, share me your site link. So, I can guide you accordingly.