Hi Anthony
There is a lot of info already posted on this site regarding the fuel delivery system, cold start system, the setting of the linkages and other aspects of the fuel system. It does take some time to search out these things, but if you use key words like "cold start valve", "linkage adjustment" etc. you will find everything you want to know has already been discussed in great detail...it is time consuming to read through them all, but it's necessary. We want to help but we try not to duplicate all this info each time someone new to the group has similar questions. I hope that doesn't sound like a put down or a put off, it's just that the real experts here, don't always have the time or inclination to repeat themselves again.
That being said, the cold start valve only operates while cranking, and is controlled by a relay and the temp. sensor mounted on the injection pump side of the engine. Some of the inj. pumps have an additional enrichment solenoid mounted on the rear of them which pushes the rack to richen for several minutes. Fuel delivery is quite important to proper running and the best place to test is to remove the fuel return line right at the gas tank to check for flow and volume...1 litre in 15 seconds being the minimum needed. The fuel pressure is less important than the volume as the injection pump is responsible for the pressure needed to open the injectors, not the fuel pump, it's just pumping in a continous loop, but needs to have the correct volume and this is often a source of running problems...a plugged outlet screen in the tank (drain tank and remove the large nut on the bottom to access) a plugged inlet screen in the fuel pump, a plugged fuel filter in the engine bay, or restrictions in the return to tank line can all cause poor running issues. The "pressure" regulator in the engine compartment is in fact a damper to lessen noise and pulsing in the system and not to regulate pressure. But first thing to determine is adequate flow, then let us know what you find and we'll go from there
Chances are the injection pump itself will be fine, so don't run out and get it rebuilt before testing everything else.
Good luck