Its not BL heli firmware that have issues with pixhawk, but rather these specific BL heli esc's as the actual hardware has some compatibility issues with Pixhawk autopilots, but not others (an issue to do with the PWM signal voltage).
The SimonK ESC's you mentioned will work well, however if you are definitely after BLheli firmware we do sell the new Emax Nano series 20A which are fully compatible with pixhawk.
As for the BEC/ No BEC issue it does not realy matter that much but usually for pixhawk you will have 1 ESC with BEC output, and 3 with no BEC. You can read more on our ESC guide
Hope that helps