I lowered my stang with Steeda Sports and I'm wondering if I should adjust the tire pressure. I run 32-34 all the way around, should I increase the pressure up front and leave the rear as is?
This is a good concept at the track, but not for daily driving. You would actually have less contact area and a harsher ride if you put the tire on max pressure, plus IMO that's kinda unsafe. No you dont have to run different tire pressure when you lower the car. I typically run 33-34lbs on the street for DD.
Forget the 44 psi max. Those numbers indicate that it's a higher quality tire, and you'd only run close to that when road-racing. The goal with tire pressures is to have the same loaded radius on the front and back wheels. That means from the hub to the ground. Since the front of the car weighs more than the rear, that's why you want more pressure in the front than the rear.
I run from 35-36 in the front and 32 in the rear. Yes, I sacrifice a bit of turn-in sharpness by not running higher, but the ride suffers too much if I go any more. I run 32 in the rear to match the radius in the front.
Basically, just start at LEAST with what Ford recommends and add more and more pressure (but not beyond max) until the ride suffers too much. Higher pressure is generally better for the tire anyway since it runs cooler - heat cycling wears out a tire and also makes it harder - less traction.