Thank you! Indeed relays seem to play an important role in my Ford Focus 2005 ZXW cold start problem. Switching around R1 (ignition relay) with next to it R3 (cooling fun high speed) resolved the problem (or hitting the fuse box during starter cranking the engine). At first, I fought R1 was bad, but after $1 substitution relay from 2006 Ford from KennyUpull junk yard that did not resolve it, I swapped them again and it worked. The quality of those relays is a mystery :)
The previous owner was doing "press a gas pedal and wait 2 minutes + dance around" routine to start it.
Not sure which one is "power hold relay" though.