On Fords the fuel pump(s) is turn on for 2 seconds when key is first turned on, I would make sure high pressure pump is coming on, although I don't think it would start or idle if either pump wasn't working.
If you let engine idle until temp is higher does it behave better?
Could be the electronic "choke" is not coming on with cold engine start.
The "choke" is computer software that advances spark timing, raise idle(via IAC valve) and runs injectors richer, until engine warms up.
If this doesn't happen then cold engine can barely run on "normal" warm engine settings.
So does idle go up and stay up at 1,000rpms with cold engine start?
This would mean "choke mode" is set.
There is a test you can do to see if an injector is stuck open, causing a rich mix.
Key on
Press gas pedal to floor and hold it there
Crank engine
Engine should NOT start, should not fire at all.
The above procedure sends computer 5volts from the TPS(gas pedal sensor), when computer see this without engine running it will shut off injectors, but not spark, this software routine allows for clearing/drying out a flooded engine.
If engine fires during this test then gas is getting into the intake from somewhere, usually leaking injector, but FPR(fuel pressure regulator) has a vacuum line to intake, and a leak at the FPR will allow gas to be sucked into the intake via that vacuum line.
Because it is easy to check, remove that vacuum line on the FPR and check it for fuel or fuel smell.
And remember, "new" no longs means "it works"; "new" now means "never been tested", so a new FPR just means it has never been tested by anyone, you are the first to see if it will work
Welcome Visitor! Please take a few seconds and 
