I know similar questions have been asked, and trust me, I've spent a few days digging around before posting something. So here it is:
There seems to be no (documented) way of adding an extra tracking number to the same item when integrating with fulfilment order based fulfillments.
You're correct on the third point, from the Fulfillment resource docs:
A fulfillment order represents a group of one or more items in an order that are to be fulfilled from the same location. A fulfillment represents work that is completed as part of a fulfillment order and can include one or more items. You can use the Fulfillment resource to manage fulfillments for both orders and fulfillment orders.
Each fulfillment supports a single tracking number. If you need to use multiple tracking numbers, then you should create separate fulfillments.
So while it is possible to have more than one fulfillment per order, you'd create separate fulfillments (with separate tracking numbers) each time.