if anyone can diagnose the problem with my car from what i have said about my cold and warm idle.. PLEASE LET ME KNOW

as of know this is my idea:

fuel pump relay
i looked at my relay and it says 6 zyl.. 6200 rpm? my car is a 190e 16v... maybe the old one broke and i guess the previous owner went to a junkyard or something and found a 2.6 fpr to replace it?

could this be why my cold start valve is not working?

i read somewhere that the voltage supply for the Cold start Valve is from this relay?

ANYONE?