It doesn’t need to be through Square Online; Any API call that calls CreateOrder will trigger the webhook. With that said, if it’s created in a way without the API, it will not trigger the webhook, it solely depends on how you’re creating the order so if you want to discuss further please let me know how you’re creating the order. Otherwise, you’ll need to create your own logic to be notified (or register for payment webhooks instead to listen for, since unpaid orders do not push to Square Dashboard or Square POS).
Since DELIVERY is not really available in the API, the details are not available unfortunately. The only way you can create a DELIVERY order is via Square Online, not the API, so the details are not through the API. There’s a few feature requests on the forums for this to be made available, but it currently doesn’t exist. As for the remaining details of the order object, you can simply retrieve it via the API when you receive the webhook via the order_id. The delivery_details will not be available, though, just to reiterate (everything else will be there; prices, items, times, etc).