Do iMessage and FaceTime show on cell phone records

iMessage and FaceTime are just data users; there is no way to identify what the data was used for; it will just appear generically as data on your phone bill.

Similarly, if you use Wi-Fi the network provider of your Wi-Fi connection to the Internet will have a record of your data use.

No.

Unless you use cellular data and are billed for that.

Deeblckk wrote:

So are you saying turn the cellular data toggle off and use Wi-Fi?

No. Wi-Fi will be used when available.