The pump is on the back of the engine, hard to see and to get too. Stand by the passenger side of the car and look at the back of the engine and you will see it, just follow the path of the belt.
Check the modulating valve - maybe sucking oil through the vacuum system and burning it as fuel.
The 3.8 Liter V6 powering the Buick Park Avenue Ultra requires only 87 octane fuel. You can use 89 octane but there is zero benefit in doing so. The Supercharged version may require 89 or 91 octane of that I am not sure. Check the owners manual and use exactly what is recommended.
Check out Crutchfield.com
Check in the air filter housing.
Owner's manual.
Electrical problem, check batt cable connections to start
check crank sensor
in the oil pan... chech for what looks like a 3/4 inch plastic nut for a wire coming out of it on the either the fron or back of the motor
Select the tire pressure info by pressing the "gage info" button, then press and hold the reset button until the display shows that the tire pressures have been reset.
check the alternator, ignition coil. or even see what the charge at the battery is.
Check your owners manual.
Check firing order