I think for authentication, iCloud can use SMS as a fallback. Just make sure you remove your iPhone from your trusted device.
Two-factor authentication is designed to make sure that you're the only person who can access your account. Learn how it works and how to turn on two-factor authentication.
support.apple.com
Yes, you will need to disable iMessage and Facetime on the iPhone prior to resetting it.
Use these steps to transfer information to your new device and, if applicable, remove your personal information from your old device.
support.apple.com
You should also disable Find my and sign out off iCloud completely on your iPhone.