You can use Find My iPhone without entering a two-factor authentication code by going to www.icloud.com/find as described in If your iPhone, iPad, or iPod touch is lost or stolen - Apple Support
I would also strongly recommend that you add other trusted devices (if you have any) and trusted phone numbers. The phone numbers can be any phone (including Androids and landlines) and can belong to a relative or friend. More information and instructions on how to add them in Two-factor authentication for Apple ID - Apple Support
Regarding turning off two factor, see the following from that same link:
If you already use two-factor authentication, you can no longer turn it off. Certain features in the latest versions of iOS and macOS require this extra level of security, which is designed to protect your information. If you recently updated your account, however, you can unenroll for a period of two weeks. Just open your enrollment confirmation email and click the link to return to your previous security settings. Keep in mind, this makes your account less secure and means that you can't use features that require a higher level of security.