Bluetooth control UMP

Am I right you can trigger recording on but not turn it off via BT? I can't.

Also will the battery be charged on the BM v-mount adaptor if the camera is connected to a power supply?

I don't know about the app, as I don't have an iPad.

But no, it won't charge the battieres on the camera, when you attach the 4-pin XLR power connector. The power does not run into battery.