The rules for shipping Lithium-ion batteries can change. Unfortunately only those people who ship such products daily and who have the necessary training will be able to answer your questions. Like I said previously I did have such training, but it covered way more than I actually needed to know so it overwhelmed me with details. I know what I need to ship what I need to ship, but I don't know about other items.
I do know that ideally the batteries need to be shipped with only about a 25% charge on them for safety to minimize the chance of a fire. I do know that the packages do require multiple labels specific to the type of battery & product you are shipping.
Unless you are shipping the item(s) to Apple you need most likely need to deal with the shippers themselves. If you are shipping items to Apple, then Apple will usually provide the exact details and necessary labels as well as a proper shipping container. If you are having issues at the shippers, then ask to speak with a manager.
Here is a UPS document covering some of the aspects for shipping Lithium-ion batteries:
https://www.ups.com/assets/resources/media/en_US/pack_ship_batteries.pdf