Is this possible without having to send a Square invoice? According to the recurring payments feature FAQ, processing recurring payments is not possible yet. I'm not sure this is out of date as there is API documentation for processing recurring payments.
If it is possible, is there a way to define that an order is recurring and what the dates/frequency in the Checkout API? Or is it expected to call the charge API with the card on file each subscription billing period?
The latter, call the API whenever you want to make a charge. Thanks for the heads up about the old FAQ! Also check out the blog post on using PHP for recurring charges: https://medium.com/square-corner-blog/recurring-charges-with-php-and-card-on-file-60f2bcb9aeac