Rented movies will appear in the Library tab of the TV app on your iPhone and other devices with the same Apple ID account. It will not appear on devices with a different Apple ID active. Rented movies can’t be shared in Family Sharing. Rented movies won’t be charged more than once, if the rental period isn’t over yet. Once you finish the rental transaction, you will be presented with a choice to ‘watch now’ or ‘watch later’. That is important for the duration of the rental period, as the start of playback sets the 48 hour countdown.
Users can’t rent on Fire TV, as the Apple TV app doesn’t support in-app purchases on that platform at this time. But if rented on a different device, then the content can be watched on Fire TV.
The rental price will be charged to your Apple ID account when you successfully complete that transaction. Any charge to your Apple ID account will go to the primary payment method associated with that account. If there is an issue with your account or payment methods, then the transaction will not finalize.
Rent movies from the Apple TV app - Apple Support