Your rear brake sounds a lot like mine does before it gets good and hot. I also think mine has been getting better as I've tried to wear it in some. The problem is, it's a rear brake ... on a motorcycle. It doesn't get all that worn even when you go out of your way to use it. I think I've come across some people claiming other pads will get rid of the noise. I just switched to regen rear breaking. Of course, you can only do that if you have the cable and software to program the motor controller.
As for the noise under drive, it's hard to say without seeing it. You've obviously got some kind of harmonic there. First, I'd download the Gates belt tension app and use it to check the belt tension if you don't have any other way. Assuming the belt tension is good, I'd run it on a stand and see if the vibration is there unloaded. If it is, feel for anything "bumpy" spots in the rotation of the wheel. Unfortunately, you probably wouldn't be able to feel anything in the motor bearings without removing the drive belt and manipulating the motor shaft directly. If everything is still smooth, I'd suspect a hormonic from the torque output of the motor, which would more than likely be a motor controller tuning issue you'd have to take up with your dealer.
That isn't an all encompassing list, but it might get your started.