I've just had exactly the same issue. I tried to solve it hardly, but appeared that only a few simple steps can resolve the situation.
- Turn on your bluetooth keyboard (or other device) and switch it co pairing mode (usually you have to press 'connect' button for that).
- In your phone settings choose the device you want to pair it with.
- In the "enter the pin for bluetooth keyboard" that you showed in screenshot in the first message, enter 0000 (I suppose you can enter any combination of digits, but I used 0000).
- Right after that press '0000' (or any other combination you entered in the previous step) ON YOUR KEYBOARD and hit enter on it.
WORKS!!!
Windows 10 phone