Hi Demos,
I find it interesting your custom board K20 isn't being recognized as a JLink with the JLink app, but it enumerates as an MBED app. Maybe try dragging and dropping the JLink OpenSDAv2.0 app into the BOOTLOADER drive instead and see if that one comes up.
Also you could try the following for loading OpenSDAv2.1:
1) Erase and then load the attached bootloader binary (OpenSDAv2.1) onto the K20 device on your custom board
2) Plug in your board and make sure it comes up as BOOTLOADER drive
3) Drag-and-drop the K22F CMSIS-DAP app into that BOOTLOADER drive (this app will debug with any device, not just K22. The MSD drag-and-drop flashing is the K22 specific part)
4) Make sure it now comes up as MBED drive
5) Try debugging with the OpenOCD configuration
6) If debugging fails, let's try the JLink app
7) Go back into Bootloader mode (hold reset while plugging in board) and into the BOOTLOADER drive that should come up, drop in the JLink OpenSDAv2.1 app
8) Unplug and plug back in your board, and look in the Device Manager to make sure you have a JLink device and COM port
9) Try debugging with a JLink configuration
Hopefully one of those will work for you. If it doesn't, let me know what step failed.
-Anthony