Bluetooth keyboard not showing battery level and function key not working
What is the model and age of your laptop?

I had some trackpad issues a month or so ago with my own Macbook, and it turned out that the battery was in need of replacement, swelling and pressing the trackpad.  Also, have you tried clearing the NVRAM?  Press the built-in keyboard keys P R option command while rebooting to clear the NVRAM.  Also it might be worthwhile to clear the system caches … hold down the shift key while rebooting to do that.  Then try re-pairing the bluetooth device and see if it is any more successful.