Fuel pump prime for quick starting?

So i have a 2000 Mustang GT i've had since about August or so, ever since i got it, the fuel pump has to be primed 2-3 times to start quickly/normally, otherwise it takes a second or two of cranking before starting and will be low idle and/or choppy for a couple seconds. but thats the only symptom, no issues after that, nothing at high rpm/speed etc just when starting. if its warm and i go to start it 30 mins after shut off it starts up fine without priming but any sort of cooldown or overnight and it does that. wouldn't think fuel pump since it runs great otherwise, maybe FPR? just a bit embarrassing and takes me longer to start so just bothers me a bit is all i can live with it if need be

as a side note the drivers window stopped working shortly after buying it, bummed since i thought i was lucky for having both windows working.... can hear it click when i push the button, but nothing. im assuming connection/ground/wiring fatigue. makes drive thru's annoying...

I'm by no means a stranger to working on my own cars lol, that's why i came here, just was a bit thrown off due to the symptoms as to where to start exactly and just wanted some other opinions, i figured pump at first and i guess it makes the most sense.

and yes 99+ was returnless, i don't remember if the reg is on the rail or pump but ill look into those either way. might even upgrade while im in there since this thing isn't gonna be "stock" forever lol

So I have an update... I was driving the car home one night and started cutting out like the fuel pump was finally going out, and when I would turn the key to run, it would run the fans, odometer show dashes, theft light flash, and no fuel pump prime. Later I noticed I also couldn’t get anything to read the computer via the OBD port (scan tool or tuner). Is the PCM bad or what’s going on here? I haven’t messed with anything wiring and everything is getting power still.