1

no recording with the bluetooth earpiece.  Is there any way to allow bluetooth recording without rooting?

2

There is a bug in the ROM of your phone related to bluetooth recording.
Boldbeast Recorder can fix the problem, unfortunately root is needed.

Please root your phone, enable the "Change Audio Control" option in the app, then you'll record calls perfectly in two directions via bluetooth. The option is visible only after you root the phone.