No problem! Ask as many questions as you need, its what we are here for. your not bothering me at all!
Yes, I have heard of fuel pumps cause cold no starts. When an engine is first started, it needs more fuel to help get things going, then if it was just idling. And a cold engine needs even more fuel (like a choke on a carburetor). Also note, that system voltage drops during cranking (which is normal) and pump output is directly related to system voltage. The higher the voltage, the higher the fuel volume/pressure and vice-versa.
So if the pump is weak, a cold start is where it will be most noticable, due to the higher fuel demand and lower system voltage. If you spray some fluid in the intake to get it started, this does two things: Gets the engine running to where it doesn't need all that extra fuel any more and also gets it running well enough the starter is no longer needed, but now the alternator is actually charging, which increases system voltage. With these two things out of the way, the pump can now generate enough fuel to run the engine.
I can't garuntee you 100% that your pump is failed because I'm not there looking at it, but after everything I have heard, I'm pretty sure that will take care of it!
Hope this helps!