Are the batteries actually used up - or just showing red in the camera? I have this occasionally where the batteries appear to be used up but actually aren't. Turning camera off, removing and replacing batteries fixed the problem.
Perhaps you could post some problem examples - SOOC with EXIF metadata intact - I find noise well controlled at 6400 ISO - unless you view at 100% and get close to the screen
Bluetooth Low Energy is designed to be on all the time - when you think about all the devices such as smart watches with small batteries that use it there can't be much impact on battery life.
Works OK on the XT-2 and according to the X-T20 manual and specifications its available on the X-T20 - just not as wide a range as when shooting stills:
http://www.fujifilm.com/products/digital_cameras/x/fujifilm_x_t20/specifications/
Yes - and Fuji considers continuous bursts to be a form of bracketing (and marks them in the same way) so its tricky to use.
I tend to leave the camera permanently on CL so every file gets marked as using Auto Bracketing.
This can be done on a computer after the files have been uploaded if you don't mind doing a little scripting.
Information about the bracketed sets are stored in the EXIF metadata.