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.