I have gone through your post and I would like to help
Try reinstalling the Keyboard and also update the BIOS
- Select the Start button, type Device Manager, and select it from the list of results.
- Look for Keyboard and expand the List
- Look for Keyboard driver then right-click it, and select Update Driver.
- Select Search automatically for updated driver software.
- If these steps don't work, try reinstalling the driver: Open Device Manager, right-click the bluetooth driver and select Uninstall. Restart your PC and Windows will attempt to reinstall the driver.